math 2413 general review for calculus last updated … · 2017-02-24 · ... 5x + 11 x 3 + 2x 2 + 6...

Math 2413 General Review for Calculus Last Updated 02/23/2016

Find the average velocity of the function over the given interval.1. y = 6x3 - 5x2 - 8, [-8, 1]

Find the slope of the curve for the given value of x.2. y = x2 + 11x - 15, x = 1

Use the graph to evaluate the limit.3. lim

x 0f(x)

4. limx 0

f(x)

1

5. Find limx (-1)-

f(x) and limx (-1)+

f(x)

Use the table of values of f to estimate the limit.

6. Let f(x) = x - 4x - 2

, find limx 4

f(x).

x 3.9 3.99 3.999 4.001 4.01 4.1f(x)

7. Let f(x) = x - 1x2 + 4x - 5

, find limx 1

f(x).

x 0.9 0.99 0.999 1.001 1.01 1.1f(x)

Give an appropriate answer.

8. Let limx 8

f(x) = 2 and limx 8

g(x) = 1. Find limx 8

9f(x) - 4g(x)7 + g(x)

.

Find the limit.9. lim

x 2(x3 + 5x2 - 7x + 1)

10. limx 0

1 + x - 1x

Find the limit, if it exists.

11. limx 1

x4 - 1x - 1

2

12. limx 9

9 - x9 - x

Provide an appropriate response.

13. The inequality 1-x22

<sin x

x< 1 holds when x is measured in radians and x < 1.

Find limx 0

sin xx

if it exists.

For the function f whose graph is given, determine the limit.14. Find lim

xf(x).

Find the limit.

15. limx -2

1x + 2

16. limx 2-

1(x - 2)2

17. limx -5-

4x2 - 25

18. limx

x2 - 5x + 11x3 + 2x2 + 6

19. limx -

-9x2 + 9x + 17-3x2 + 6x + 14

20. limx -

4x3 + 4x2

x - 5x2

3

Divide numerator and denominator by the highest power of x in the denominator to find the limit.

21. limx

3x-1 - 5x-3

2x-2 + x-5

22. limt

16t2 - 64t - 4

Find all points where the function is discontinuous.23.

Provide an appropriate response.24. Is f continuous at x = 0?

f(x) =x3,-3x,3,0,

-2 < x 00 x < 22 < x 4x = 2

Find the intervals on which the function is continuous.

25. y = 1x2 + 10x + 35

26. y = x + 2x2 - 6x + 8

4

Provide an appropriate response.27. Is f continuous on (-2, 4]?

f(x) =x3,-4x,6,0,

-2 < x 00 x < 22 < x 4x = 2

28. Use the Intermediate Value Theorem to prove that -2x3 - 7x2 + 2x + 1 = 0 has a solution between -1 and 0.

Find numbers a and b, or k, so that f is continuous at every point.29.

f(x) = x2, ax + b,x + 12,

x < -1-1 x 4x > 4

Solve the problem.30. Select the correct statement for the definition of the limit: lim

x x0f(x) = L

means that __________________

Use the graph to find a > 0 such that for all x, 0 < x - x0 < f(x) - L < .31.

y = 4x - 17.2

7

6.8

21.95 2.05

NOT TO SCALE

f(x) = 4x - 1x0 = 2L = 7

= 0.2

5

32.

y = x

1.981.731.48

2.1975 3 3.9275

NOT TO SCALE

f(x) = xx0 = 3

L = 3

=14

33.

y = x - 3

1.251

0.75

3.5625 4 4.5625

NOT TO SCALE

f(x) = x - 3x0 = 4L = 1

=14

6

34.

y = x2

5

4

3

21.73 2.24

NOT TO SCALE

f(x) = x2x0 = 2L = 4

= 1

A function f(x), a point x0, the limit of f(x) as x approaches x0, and a positive number is given. Find a number > 0 suchthat for all x, 0 < x - x0 < f(x) - L < .

35. f(x) = 4x2, L =36, x0 = 3, and = 0.1

Prove the limit statement

36. limx 5

x2 - 25x - 5

= 10

37. limx 7

3x2 - 19x- 14x - 7

= 23

38. limx 5

1x

=15

Find an equation for the tangent to the curve at the given point.39. y = x2 + 2, (2, 6)

40. f(x) = 2 x - x + 3, (4, 3)

Calculate the derivative of the function. Then find the value of the derivative as specified.

41. f(x) = 8x + 2

; f (0)

7

Solve the problem.42. The graph of y = f(x) in the accompanying figure is made of line segments joined end to end. Graph the

derivative of f.

The figure shows the graph of a function. At the given value of x, does the function appear to be differentiable,continuous but not differentiable, or neither continuous nor differentiable?

43. x = -1

8

44. x = 1

Compare the right-hand and left-hand derivatives to determine whether or not the function is differentiable at the pointwhose coordinates are given.

45.

y = x y = 2x

Find the derivative.46. y = 6x2 + 7x + 2ex

a. 12x + 2ex b. 12x + 7 + 2ex c. 12x + 7 + ex d. 6x + 2ex

Find y .47. y = (5x - 4)(2x3 - x2 + 1)

48. y = (x2 - 5x + 2)(5x3 - x2 + 5)

Find an equation of the tangent line at x = a.49. y = x2 - x; a = 2

9

50. y = x3 - 25x + 5; a = 5

Find the second derivative.51. y = 7x3 - 2x2 + 7

52. y = 8x3 - 6x2 + 6ex

Find y .53. y = (2x - 5)(2x3 - x2 + 1)

54. y = x + 1x

x - 1x

Find the derivative of the function.

55. y = x2 + 2x - 2x2 - 2x + 2

56. y = (x + 4)(x + 1)(x - 4)(x - 1)

Find the derivative.

57. s = 2et

2et + 1

58. y = 5x2e-x

Find the indicated derivative.59. Find y if y = 3x sin x.

The function s = f(t) gives the position of a body moving on a coordinate line, with s in meters and t in seconds.60. s = 4t2 + 2t + 9, 0 t 2

Find the body's displacement and average velocity for the given time interval.

Solve the problem.61. At time t, the position of a body moving along the s-axis is s = t3 - 15t2 + 48t m. Find the body's acceleration

each time the velocity is zero.

62. Suppose that the dollar cost of producing x radios is c(x) = 400 + 20x - 0.2x2. Find the marginal cost when 40radios are produced.

10

Suppose that the functions f and g and their derivatives with respect to x have the following values at the given values ofx. Find the derivative with respect to x of the given combination at the given value of x.

63.x f(x) g(x) f (x) g (x)3 1 9 8 74 -3 3 5 -5

f(g(x)), x = 4

64.x f(x) g(x) f (x) g (x)3 1 9 8 34 -3 3 5 -5

f(x) + g(x), x = 3

Find the derivative of the function.65. y = (x + 1)2(x2 + 1)-3

66. h(x) = cos x1 + sin x

6

Find y .

67. y = 10 +4x

4

68. y = sin(4x2ex)

Use implicit differentiation to find dy/dx.

69. x + yx - y

= x2 + y2

70. xy + x + y = x2y2

At the given point, find the slope of the curve or the line that is tangent to the curve, as requested.71. x5y5 = 32, tangent at (2, 1)

Use implicit differentiation to find dy/dx and d2y/dx2.72. y2 - x2 = 8

73. xy + 3 = y, at the point (4, -1)

At the given point, find the line that is normal to the curve at the given point.74. x5y5 = 32, normal at (2, 1)

Find the derivative of y with respect to x, t, or , as appropriate.75. y = ln(ln 2x)

11

76. y = ln 1 - x(x + 3)4

Find the derivative of y with respect to the independent variable.77. y = 4x

Find the derivative of the function.78. y = log |2 - x|

79. f(x) = log5 (x6 + 1)

Use logarithmic differentiation to find the derivative of y.

80. y = xx - 4

81. y = x(x + 3)(x + 4)

Use logarithmic differentiation to find the derivative of y with respect to the independent variable.82. y = (x + 2)x

83. y = (sin x)cos x

Find the derivative of y with respect to x.

84. y = tan-1 6x3

85. y = 2 sin-1 (4x4)

Find the value of df-1/dx at x = f(a).86. f(x) = x3 - 3x2 - 6, x 2, a = 4

87. f(x) = x2 - 4x + 7, x 2, a = 5

Solve the problem.88. A wheel with radius 3 m rolls at 11 rad/s. How fast is a point on the rim of the wheel rising when the point is

/3 radians above the horizontal (and rising)? (Round your answer to one decimal place.)

Solve the problem. Round your answer, if appropriate.89. One airplane is approaching an airport from the north at 189 km/hr. A second airplane approaches from the east

at 228 km/hr. Find the rate at which the distance between the planes changes when the southbound plane is 36km away from the airport and the westbound plane is 15 km from the airport.

90. A man 6 ft tall walks at a rate of 7 ft/sec away from a lamppost that is 14 ft high. At what rate is the length of hisshadow changing when he is 45 ft away from the lamppost? (Do not round your answer)

12

91. The volume of a rectangular box with a square base remains constant at 1100 cm3 as the area of the baseincreases at a rate of 9 cm2/sec. Find the rate at which the height of the box is decreasing when each side of thebase is 19 cm long. (Do not round your answer.)

92. The radius of a right circular cylinder is increasing at the rate of 6 in./sec, while the height is decreasing at therate of 9 in./sec. At what rate is the volume of the cylinder changing when the radius is 11 in. and the height is 7in.?

Determine all critical points for the function.93. f(x) = x2 + 2x + 1

94. f(x) = x3 - 12x + 3

95. f(x) = -3xx - 4

Find the absolute extreme values of the function on the interval.96. g(x) = -x2 + 11x - 28, 4 x 7

97. g(x) = 6 - 8x2, -4 x 5

Find the absolute extreme values of the function on the interval.

98. f(x) = ln(x + 2) + 1x

, 1 x 9

99. f(x) = ex - x, -2 x 2

Find the extreme values of the function and where they occur.100. y = x3 - 12x + 2

101. y = 1x2 + 1

102. y = 8xx2 + 1

103. y = x3 - 3x2 + 5x - 6

104. y = x + 1x2 + 3x + 3

Solve the problem.105. Sketch a continuous curve y = f(x) with the following properties:

f(2) = 3; f (x) > 0 for x > 4; and f (x) < 0 for x < 4 .

13

Find the largest open interval where the function is changing as requested.

106. Increasing f(x) = 1x2 + 1

107. Decreasing f(x) = x3 - 4x

Use the graph of the function f(x) to locate the local extrema and identify the intervals where the function is concave upand concave down.

108.

109.

14

Graph the equation. Include the coordinates of any local extreme points and inflection points.110. y = 10x2 + 20x

111. y = 8xx2 + 4

112. y = 2x3 + 3x2 - 12x

15

113. y = x2

x2 + 2

Sketch the graph and show all local extrema and inflection points.114. y = |x2 - 2x|

Solve the problem.115. From a thin piece of cardboard 40 in. by 40 in., square corners are cut out so that the sides can be folded up to

make a box. What dimensions will yield a box of maximum volume? What is the maximum volume? Round tothe nearest tenth, if necessary.

116. A company is constructing an open-top, square-based, rectangular metal tank that will have a volume of 65 ft3.What dimensions yield the minimum surface area? Round to the nearest tenth, if necessary.

117. A private shipping company will accept a box for domestic shipment only if the sum of its length and girth(distance around) does not exceed 90 in. Suppose you want to mail a box with square sides so that itsdimensions are h by h by w and it's girth is 2h + 2w. What dimensions will give the box its largest volume?

16

118. A window is in the form of a rectangle surmounted by a semicircle. The rectangle is of clear glass, whereas thesemicircle is of tinted glass that transmits only one-fourth as much light per unit area as clear glass does. Thetotal perimeter is fixed. Find the proportions of the window that will admit the most light. Neglect the thicknessof the frame.

119. A long strip of sheet metal 12 inches wide is to be made into a small trough by turning up two sides at rightangles to the base. If the trough is to have maximum capacity, how many inches should be turned up on eachside?

120. The 9 ft wall shown here stands 30 feet from the building. Find the length of the shortest straight beam that willreach to the side of the building from the ground outside the wall.

9' wall

30'

121. A rectangular field is to be enclosed on four sides with a fence. Fencing costs $5 per foot for two opposite sides,and $6 per foot for the other two sides. Find the dimensions of the field of area 850 ft2 that would be thecheapest to enclose.

17

122. Find the number of units that must be produced and sold in order to yield the maximum profit, given thefollowing equations for revenue and cost:R(x) = 60x - 0.5x2C(x) = 9x + 9.

123. Suppose a business can sell x gadgets for p = 250 - 0.01x dollars apiece, and it costs the businessc(x) = 1000 + 25x dollars to produce the x gadgets. Determine the production level and cost per gadget requiredto maximize profit.

Find the linearization L(x) of f(x) at x = a.124. f(x) = 4x2 - 5x - 4, a = 5

125. f(x) = 16x + 5

, a = 0

126. f(x) = x + 1x

, a = 3

Solve the problem.

127. V = 43

r3, where r is the radius, in centimeters. By approximately how much does the volume of a sphere

increase when the radius is increased from 2.0 cm to 2.1 cm? (Use 3.14 for .)

128. The diameter of a tree was 10 in. During the following year, the circumference increased 2 in. About how muchdid the tree's diameter increase? (Leave your answer in terms of .)

Determine whether the function satisfies the hypotheses of the Mean Value Theorem for the given interval.129. f(x) = x1/3, -1,3

130. g(x) = x3/4, 0,3

Find the value or values of c that satisfy the equation f(b) - f(a)b - a

= f (c) in the conclusion of the Mean Value Theorem for

the function and interval.131. f(x) = x2 + 3x + 2, [1, 2]

132. f(x) = x + 96x

, [6, 16]

a. 6, 16 b. 4 6 c. 0, 4 6 d. -4 6, 4 6

133. f(x) = ln (x - 2), [3, 6] Round to the nearest thousandth.

18

Use l'Hopital's Rule to evaluate the limit.

134. limx /3

cos x - 12

x -3

135. limx 0

sin 2xtan 3x

136. limx

x sin 11x

137. limx

x2 + 3x - x

Find the limit.

138. limx 0

1 + 2x5

x

139. limx

(ln x)5/x

Use a calculator to compute the first 10 iterations of Newton's method when applied to the function with the given initialapproximation. Make a table for the values. Round to six decimal places.

140. f(x) = x3 + x - 9; x0 = 1

Use Newton's method to approximate all the intersection points of the pair of curves. Some preliminary graphing oranalysis may help in choosing good initial approximations. Round to six decimal places.

141. y = x3 - 2x2 and y = x2 - 1

Use Newton's method to find an approximate answer to the question. Round to six decimal places.

142. Where are the inflection points of f(x) = 54

x4 +83

x3 - 10x2 + 4 located?

A fixed point of f is a value of x that satisfies the equation f(x) = x; it corresponds to a point at which the graph of fintersects the line y = x. Find all the fixed points of the function. Use preliminary analysis and graphing to determinegood initial approximations. Round approximations to six decimal places.

143. f(x) = x2 - 1

Find all the roots of the function. Use preliminary analysis and graphing to determine good initial approximations.Round to six decimal places.

144. f(x) = ln(2x) - 2x2 + 3x + 1

19

Find the most general antiderivative.

145. (6x3 - 4x + 5) dx

146. x x + xx2

dx

147. 6

1 - x2-

5x

dx

148. 7x2 + 1

-6x

dx

Solve the initial value problem.

149. d2ydx2

= 5 - 5x, y (0) = 8, y(0) = 2

150. d3ydx3

= 9; y (0) = -4, y (0) = 4, y(0) = 5

Provide an appropriate response.151. The position of an object in free fall near the surface of the plane where the acceleration due to gravity has a

constant magnitude of g (length-units)/sec2 is given by the equation:

s = -12

gt2 + v0t + s0, where s is the height above the earth, v0 is the initial velocity, and s0 is the initial

height. Give the initial value problem for this situation. Solve it to check its validity. Remember the positivedirection is the upward direction.

Estimate the value of the quantity.152. The velocity of a projectile fired straight into the air is given every half second. Use right endpoints to estimate

the distance the projectile travelled in four seconds.

Time(sec)

Velocity(m/sec)

00.51.01.52.02.53.03.54.0

128123.1118.2113.3108.4103.598.693.788.8

Use a finite approximation to estimate the area under the graph of the given function on the stated interval as instructed.153. f(x) = x2 between x = 0 and x = 2 using a right sum with two rectangles of equal width.

20

154. f(x) = 1x

between x = 2 and x = 7 using a right sum with two rectangles of equal width.

Graph the function f(x) over the given interval. Partition the interval into 4 subintervals of equal length. Then add to

your sketch the rectangles associated with the Riemann sum 4

k=1f(ck) xk , using the indicated point in the kth

subinterval for ck.

155. f(x) = x2 - 3, [0, 8], midpoint

156. f(x) = x2 - 3, [0, 8], right-hand endpoint

Solve the problem.

157. Suppose that 4

2f(x) dx = 3. Find

4

4f(x) dx and

2

4f(x) dx .

Compute the definite integral as the limit of Riemann sums.

158.2

1(3x - 1) dx

21

Find the area of the shaded region.159.

160.

Evaluate the integral.

161./2

025 sin x dx

162.3 /4

- /45 sec tan d

Find the total area of the region between the curve and the x-axis.

163. y = 3x3

; 1 x 3

Find the derivative.

164. ddx

x

114t9 dt

165. y =x

0

dt2t + 5

166. ddt

sin t

0

116 - u2

du

Find the average value of the function over the given interval.167. y = x2 - 6x + 6; [0, 6]

22

Evaluate the integral using the given substitution.

168. dx4x + 8

, u = 4x + 8

Evaluate the integral.

169. x dx(7x2 + 3)5

170. 9x2 49 + 4x3 dx

Use the substitution formula to evaluate the integral.

171.1

0

6 r dr

16 + 3r2

172./2

0

cos x(5 + 4 sin x)3

dx

173.1

0

dx

9 - x2

Find the area enclosed by the given curves.174. Find the area of the region between the curve y = 2x/(1 + x2) and the interval -4 x 4 of the x-axis.

Evaluate the integral by using multiple substitutions.

175. 8 + sin2 (x - 8) sin (x - 8) cos (x - 8) dx

23

Answer KeyTestname: GENERAL CAL REVIEW

1. 3772. slope is 133. does not exist4. -25. -2; -76.

x 3.9 3.99 3.999 4.001 4.01 4.1f(x) 3.97484 3.99750 3.99975 4.00025 4.00250 4.02485

; limit = 4.0

7.x 0.9 0.99 0.999 1.001 1.01 1.1

f(x) 0.1695 0.1669 0.1667 0.1666 0.1664 0.1639 ; limit = 0.1667

8. 74

9. 1510. 1/211. 412. Does not exist13. 114. -215. Does not exist16.17.18. 019. 320.21.22. 423. x = 124. Yes25. continuous everywhere26. discontinuous only when x = 2 or x = 427. No28. Let f(x) = -2x3 - 7x2 + 2x + 1 and let y0 = 0. f(-1) = -6 and f(0) = 1. Since f is continuous on [-1, 0] and since y0 = 0 is

between f(-1) and f(0), by the Intermediate Value Theorem, there exists a c in the interval (-1 , 0) with the propertythat f(c) = 0. Such a c is a solution to the equation -2x3 - 7x2 + 2x + 1 = 0.

29. a = 3, b = 430. if given any number > 0, there exists a number > 0, such that for all x,

0 < x - x0 < implies f(x) - L < .31. 0.0532. 0.802533. 0.437534. 0.2435. 0.00416

24


36. Let > 0 be given. Choose = . Then 0 < x - 5 < implies thatx2 - 25x - 5

- 10 =(x - 5)(x + 5)

x - 5- 10

= (x + 5) - 10 for x 5= x - 5 < =

Thus, 0 < x - 5 < implies that x2 - 25x - 5

- 10 <

37. Let > 0 be given. Choose = /3. Then 0 < x - 7 < implies that3x2 - 19x- 14

x - 7- 23 =

(x - 7)(3x + 2)x - 7

- 23

= (3x + 2) - 23 for x 7= 3x - 21= 3(x - 7)= 3 x - 7 < 3 =

Thus, 0 < x - 7 < implies that 3x2 - 19x- 14x - 7

- 23 <

38. Let > 0 be given. Choose = min{5/2, 25 /2}. Then 0 < x - 5 < implies that1x

-15

=5 - x5x

=1x

·15

· x - 5

<1

5/2·

15

·252

=

Thus, 0 < x - 5 < implies that 1x

-15

<

39. y = 4x - 2

40. y = -12

x + 5

41. f (x) = -8

(x + 2)2; f (0) = -2

42.

43. Continuous but not differentiable

25


44. Neither continuous nor differentiable45. Since limx 0+ f (x) = 2 while limx 0- f (x) = 1, f(x) is not differentiable at x = 0.

46. b47. 40x3 - 39x2 + 8x + 548. 25x4 - 104x3 + 45x2 + 6x - 2549. y = 3x - 450. y = 50x - 24551. 42x - 452. 48x - 12 + 6ex

53. 16x3 - 36x2 + 10x + 2

54. 2x + 2x3

55. y =-4x2 + 8x

(x2 - 2x + 2)2

56. y =-10x2 + 40

(x - 4)2(x - 1)2

57. 2et

(2et + 1)2

58. 5xe-x(2 - x)59. y = 6 cos x - 3x sin x60. 20 m, 10 m/sec61. a(2) = -18 m/sec2, a(8) = 18 m/sec262. $463. -40

64. 112 10

65. -2(x + 1)(2x2 + 3x - 1)(x2 + 1)4

66. -6 cos5 x(1 + sin x)6

67. 192x4

10 +4x

2+

32x3

10 +4x

3

68. 4(x2 + 4x + 2)ex cos(4x2ex) - 16xe2x(x3 + 4x2 + 4x) sin(4x2ex)

69. x(x - y)2 + yx - y(x - y)2

70. 2xy2 - y - 1-2x2y + x + 1

71. y = -12

x + 2

72. dydx

=xy

; d2ydx2

=y2 - x2

y3

26


73. dydx

=13

; d2ydx2

= -29

74. y = 2x - 3

75. 1x ln 2x

76. 3x - 7(x + 3)(1 - x)

77. 4x ln 4

78. -1

ln 10 (2 - x)

79. 6x5

(ln 5) (x6 + 1)

80. 12

xx - 4

1x

-1

x - 4

81. x(x + 3)(x + 4) 1x

+1

x + 3+

1x + 4

82. (x + 2)x ln(x + 2) + xx + 2

83. (sin x)cos x(cos x cot x - sin x ln (sin x))

84. 1836x2 + 9

85. 32x3

1 - 16x8

86. 124

87. 16

88. 16.5 m/s89. -262 km/hr

90. 214

ft/sec

91. 9900130321

cm/sec

92. -165 in.3/sec93. x = -194. x = -2 and x = 295. x = 4

96. absolute maximum is 94

at x = 112

; absolute minimum is 0 at 7 and 0 at x = 4

97. absolute maximum is 6 at x = 0; absolute minimum is -194 at x = 5

98. absolute minimum value is ln 4 + 12

at x = 2; absolute maximum value is ln 11 +19

at x = 9

99. absolute minimum value is 1 at x = 0; absolute maximum value is e2 - 2 at x = 2

27


100. Local maximum at (-2, 18), local minimum at (2, -14).101. Absolute maximum value is 1 at x = 0.102. Absolute minimum value is - 4 at x = -1. Absolute maximum value is 4at x = 1.103. None

104. Absolute maximum is 13

at x = 0; absolute minimum is - 1 at x = -2.

105. Answers will vary. A general shape is indicated below:

106. (- , 0)

107. -2 3

3, 2 3

3108. Local minimum at x = 1; local maximum at x = -1; concave up on (0, ); concave down on (- , 0)109. Local minimum at x = 3 ; local maximum at x = -3 ; concave up on (0, ); concave down on (- , 0)110. local minimum: (-1,-10)

no inflection points

28


111. local minimum: (-2, -2)local maximum: (2, 2)inflection points: (0, 0), (-2 3, -2 3),

(2 3, 2 3)

112. local minimum: (1, -7)local maximum: (-2, 20)

inflection point: -12

, 132

113. local minimum: (0, 0)

inflection points: -6

3, 1

4, 6

3, 1

4

29


114. Local minima: (0, 0), (2, 0)Local maximum: 1, 1No inflection points

115. 26.7 in. × 26.7 in. × 6.7 in.; 4740.7 in3116. 5.1 ft × 5.1 ft × 2.5 ft117. 20 in. × 20 in. × 15 in.

118. widthheight

=16

8 + 3119. 3 in.120. 52.3 ft121. 31.9 ft @ $5 by 26.6 ft @ $6122. 51 units123. 11,250 gadgets at $137.50 each124. L(x) = 35x - 104

125. L(x) = -625

x + 15

126. L(x) = 89

x + 23

127. 5.0 cm3

128. 2 in.

129. No130. Yes

131. 32

132. b133. 4.164

134. -3

2

135. 23

136. 11

137. 32

138. 1

30


139. 1140.

k xk0 1.0000001 2.7500002 2.1358843 1.9397934 1.9203575 1.9201756 1.9201757 1.9201758 1.9201759 1.92017510 1.920175

141. x -0.532089, 0.652704, 2.879385142. x -1.805252, 0.738586143. x -0.618034, 1.618034144. x 0.129105, 2.082625

145. 32

x4 - 2x2 + 5x + C

146. 2 x -2x

+ C

147. 6 sin-1 x - 5 ln |x| + C148. 7 tan-1 x - 6 ln |x| + C

149. y = 52

x2 -56

x3 + 8x + 2

150. y = 32

x3 - 2x2 + 4x + 5

151. d2sdt2

= -g , s (0) = v0, s(0) = s0

152. 423.8 m153. 5

154. 115126

31


155.

156.

157. 0; -3

158. 72

159. 233

160. 36161. 25162. -10 2

163. 43

164. 7x4

165. 12x + 5

166. cos t16 - sin2 t

167. 0

168. 12

4x + 8 + C

32


169. -156

(7x2 + 3)-4 + C

170. 35

9 + 4x3 5/4+ C

171. 2 19 - 8

172. 72025

173. sin-1 13

174. 2 ln 17

175. 13

(8 + sin2 (x - 8))3/2+ C

33

math 2413 general review for calculus last updated … · 2017-02-24 · ... 5x + 11 x 3 + 2x 2 + 6...

Documents