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3. Fmd the surface area o f the sohd generated by

revolvmg

a cun e Region bounded by

y

= smx , X = 0, X = - and the x-axis about

the X axis

4.

Find the length o f the curve y = coshx from x = -3 to x = 3

Al

I

a i /

5. Prove that sinh2x = 2sinhxcoshx

/•A

-2-



6. Find the area o f the region bounded by y =sinhx

,

x = 0, x = 5 and,.th^-axis

7. Usehyperbohc functions to evaluate integrals

a)

)-2

1^

b)

4dx

A

8.

Find

y'

i f

a) y = 2cosh(2x + 5)

b)-y

=

coth(3x)

•



10. Fmd the surface area o f the region formed by revolvmg

y = 1 and y = 2. about the y-axis

6

i

11. Sketch the graphs

a) y = smh 'x

b) y = cosh 'x

the

portion

o f

the sphere

between



12. A suspension bridge cable is hung betv - een tv.-o towers that are 200 ft apart as shown. The cable

is

. shape

of a catennar}

cun'e

whose equation is y = 150cosh(x/l 50) Find the length of the cable

1 iT1 iT

rrrUU

•

L

1)

13. Change the foUowkig curve to parametric form and use it to vsTite an equation which would

translate the graph to a new

origin

at (3,4)

r

=

sin2©

14.

Rotate the graph of r =sin2e

thru

the following angles (sketch)

(give new equations)

a) 45°

b)

-30°

1 / :



15.

A bread is sliced as shoATO. Find the surface area

of

the tv\'o pieces, one is an piece

Wliich

piece has the greatest surface

area

(section from 0 to 1 or

3

to 4)

y=16-x2



Newton's Law of Cooling

A cup of

coffee

cools down from 350 to 150 in 20 minutes

in a

room of

temp

70

a) Find

the temperature of the

coffee

after 30 minutes (do algebraically

and

show

work)

7

CI

7

b)

When

will the temperture of the coffee by 100



17.

Find

the total pressure exerted against

a

dam

in

the shape of

a

rectangle which lies

just below the water level The dimensions of the dam are 10 tby 40 ft



18. Find the length of the ellipse described by the equations 4x +

9y =36

^^•S a :r

^^^y

1

19.

If

you invest 5000 at an interest rate of 8% compounded continuously then

Find p

I

- • ^ jc

a The total value of your account after 12 years

b Use the rule of J2 to fmd how many years it will

take

the money to double

t7 ^ .

...

c Do

part

b using formula and compare results



20. A

triangular

dam is located as shown Find

10

a) Total force against dam

5

b) Find total force on the top half of the dam

21.

Use

calculator

to convert

from

polar

to

rectangular

form

a) Given

polar

coordinates are (3, 122°) Go to

angle

key and look for

P

^ R, 1*5 S

b) Given

rectangular

coordinates

are

(4,5)

Go

to angle key

and

look for

R ^ P r

fc^- ^ j

R-^ P

5 I • 5 ^



gxtra

Crg<iit

Write a taylor series

for sinhx

Write

a

taylor

series

for coshx

Find

the

sum

of the

areas

of

all

the triangles Triangles are formed

by

joining

all

the

midpts

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