7/28/2019 1-1 Limits,Differentiation,Rate of Change, Slope

1/7

I. Limits, Differentiation, Rate of Change, Slope

Questions AnswersChoices

A B C D

1 Evaluate B 0 1 2 3

2 Simplify the expression B 1 8 0 16

3

Evaluate the following limit,

A 0

4

Evaluate the limit

C

0 undefined infinity

5Evaluate the limit

B 1 0e infinity

6

Evaluate the following limit,

A1 indefinite 0 2

7 Evaluate: B 0 1/2 2 -1/2

8

Evaluate the following limit

Dinfinity 0

9 Find B

7/28/2019 1-1 Limits,Differentiation,Rate of Change, Slope

2/7

I. Limits, Differentiation, Rate of Change, Slope

10 Find A

11

Find C

12

Evaluate the first derivative of theimplicit function:

B

13

Find the derivative of with

respect to x. A

14If a is a simple constant, what is thederivative of A

15Find the derivative of the function

with respect to x . D

16

What is the derivative of the

expression A 0

17 Find the derivative of B

7/28/2019 1-1 Limits,Differentiation,Rate of Change, Slope

3/7

I. Limits, Differentiation, Rate of Change, Slope

18

Given the

equation: ( ) C

19Find the derivatives with respect to x B

20

Differentiate

B -2ax 2ax 2ax+b ax+2b

21 Find C

22 Evaluate the differential of D

23 If , what is ? D

24 Find : B

25 The derivative of is: C

26Find the derivative of withrespect to x. B [ ] [ ] [ ] [ ]

27What is the first derivative of

D

28 If , find ? C

7/28/2019 1-1 Limits,Differentiation,Rate of Change, Slope

4/7

I. Limits, Differentiation, Rate of Change, Slope

29Find the second derivative of

B 96 0.375 -0.25 -0.875

30

Given the function , find the value of the first

derivative at A 7 7 8

31

Given the function find

the value of the first derivative at A 6 7 8

32

Find the partial derivatives with

respect to x

of the function A

33

Find the point in the parabolaat which the rate of change

of the ordinate and abscissa are equal A (1,2) (2,1) (4,4) (-1,4)

34Find the slope of the line tangent tothe curve A 1 1/2 1/3 1/4

7/28/2019 1-1 Limits,Differentiation,Rate of Change, Slope

5/7

I. Limits, Differentiation, Rate of Change, Slope

35

Determine the slope of the curve

A 3/5 -2/5 -3/5 2/5

36

Find the slope of the tangent to the parabola at a point on the

curve where . B 0 1 1/4 -1/2

37

Find the slope of the ellipseat

the point where C -0.1654 -0.1538 -0.1768 -0.1463

38

Find the slope of the tangent to thecurve through point (2,16) C 20 1/24 24 1/20

39

Find the slope of the tangent to thecurve through the point(-2,4). A -3/2 3/2 2/3 -2/3

40

Find the slope of the line whose parametric equations are and

. B -4 1/4 4 -1/4

41What is the slope of the curve

at (1,0) A 2/5 5/2 -2/5 -5/2

7/28/2019 1-1 Limits,Differentiation,Rate of Change, Slope

6/7

I. Limits, Differentiation, Rate of Change, Slope

42

Find the slope of the curve

at (0,12). B 0.67 1.5 1.33 0.75

43Find the acute angle that the curve

cut the x-axis A 77 o 75o 79o 120 o

44Find the angle that the line

makes with the x- axis. D 74.77 o 4.5 o 47.77 o 77.47 o

45

Find the equation of the tangent to the

curve through the point(8,12) A

46What is the radius of curvature at

point (1,2) of the curve C 6.21 5.21 5.66 6.66

47

What is the radius of the curvature at point (1,2) of the curve

. C 1.5707 1

48Determine the radius of curvature at(4,4) of the curve D 24.4 25.4 23.4 22.4

49Find the radius of curvature of thecurve at (1,1) D 4.72 3.28 4.67 5.27

7/28/2019 1-1 Limits,Differentiation,Rate of Change, Slope

7/7

I. Limits, Differentiation, Rate of Change, Slope

50

The chords of the ellipsehaving equal slopes of

1/5 are bisected by its diameter.

Determine the equation of thediameter of the ellipse.

D