could you do my calculus practice exam so that i have answer to check

(1) [ /6]

(2) [ /6]

(3) [ /10]

Write it in the form

(4) [ /6]

(a) Plot the slope field for

at each of the 25 points on

the grid where t and y are

(b) sketch the particular

solution with

(c) What is the long term behavior of this solution ?

y

t

70

Put final answers in boxes on this page. Show high quality work in the blue book for all answers.

Math 34B

Prof D.A.R.Y.L.

Quality

Bonus SCORE

Tardis

2

PRINT

NAME

version

no calculators

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At the end of the exam place this page INSIDE the blue book, and then put the bluebook inside the envelope.

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Signature

Find the x and y values which give a local minimum of

x= y=

Find the equation of the tangent plane to

What is the change in f(x,y) to first

order when (x,y) is changed from

to

z=

Allo ns-

y !

(5) [ /8 ] Find the local minimum and maximum of the

function below. Use the second derivative test.

At local min:

At local max:

Red

FinalWinter 2014

∫ 2

0 a + 6x2 dx =

∫

16e−8x dx =

d dx

(

4x5e3x )

=

f(x, y) = 5e2x sin(3y)

fx(x, y) =

fy(x, y) =

fxy(x, y) =

f(x, y) = 2x2 + xy + y2 − 4x + 3y − 7

∂f ∂x

=

∂f ∂y

=

z = f(x, y) at (x, y) = (1, 0)

z = mx + ny + b

f(x, y)

(1, 0) (1 + ∆x, ∆y)

∆f =

y′(t) = y + t

0, ±0.5, ±1

y(−0.5) = 0

f(x) = 9x−1 + x + 7

f ′(x) =

f ′′(x) =

x f(x)

n =

has a rectangular base measuring 2 meters by 5 meters.

It is meters high.

Initially it contains of liquid detergent.

Then water is pumped into the tank so that after t hours the rate

water enters the tank is The water and detergent

are mixed to produce a liquid.

(b) What is the area of the

shaded region ?

(6) [ /6]

(a) What is the equation

of the sine wave shown ?

(7) [ /6]

y

t

The diagram shows a sine wave

(a) What is the solution of

with

(b) What is the solution of

(c) Substitute into the equation

and use this to find

the two values of n which give a solution

0

(8) [ /6] A colony of bacteria is growing. The mass after

t hours is grams. Initially there are grams and after

3 hours this has increased to grams. The mass satisfies

the equation

(10)[ /10] A rectangular water tank

(c) How many hours until

the tank is full ?

(d) After how many hours

does the tank contain 50%

water and 50% detergent ?

(b) What is the height of

liquid in the tank after t hours ?

(e) What is the average

height of liquid in the tank

during the first 2 hours ?

hrs

m

(c) What is the integral you

did for (b) ?

(9) [ /6] A meteor enters the Earth’s atmosphere with an

initial velocity of The velocity t seconds later is

and satisfies the equation

Initially the acceleration of the meteor is

(a) What is k ?

(b) What is the velocity after

t seconds ?

(c) What is the terminal velocity

of the meteor ?

(d) How many seconds after entering

the atmosphere until the velocity is

(a) What is k ?

(b) What is the mass

after t hours ?

(c) How many hours

does it take for the

mass to double ?

k=

=

hrs

m

(a) How many of water

are in the tank after t hours ?

[ hint acceleration ]

or

Red

24

10

y(t) = A sin(Bt) + C

y(t)=

y(t)=

y(t)=

∫

y′(t) = ky(t)

y(0) = 4 y′(0) = 8

y′(t) = 3t2 − 7

with y(1) = 8

y′′(t) − 5y′(t) + 6y(t) = 0

y = ent

m(t)

m(t) 2

7

m′(t) = km(t)

7200 ms−1

v(t) ms−1 v′(t) = k(200 − v(t))

−1000 ms−2

v(t) =

k =

ms−1

3700 ms−1

= v′(t)

18

20 m3

20t m3 per hour.

m3 m3