July 23, 2017

The ordering and transportation cost C of the components used in manufacturing a

product is given by where C is measured in thousands of

dollars and x is the order size in hundreds. Find the order size that minimizes the cost.

Round your answer to the nearest unit.

A) 58 hundreds

B) 56 hundreds

C) 53 hundreds

D) 55 hundreds

E) 60 hundreds

Find the general solution of the first-order linear differential equation.

A)

B)

C)

D)

E)

Find the derivative of the function.

A)

B)

C)

D)

E) none of the above

Find the limit (if it exists):

A)

B)

C) 0

D)

E)

Estimate the slope of the line from the graph.

A)

B) 2

C) 5

D)

E)

After t years, the value of a car that originally cost 19,000 depreciates so that each

year it is worth of its value for the previous year. Find a model for V(t), the value of

the car after t years.

A) V(t) = 19,000

B) V(t) = 19,000t

C) V(t) = 19,000

D) V(t) = 19,000

E) V(t) = 19,000t

Complete the table and use the result to estimate the limit.

x

f(x)

A) 0.121736

B) 0.101736

C) "0.138264

D) "0.008264

E) "0.118264

Write an expression for the nth term of the sequence .

A)

B)

C)

D)

E)

Find the derivative of the following function.

A)

B)

C)

D)

E)

Find a and d for such that the graph of f matches the figure.

A)

B)

C)

D)

E)

Use a calculator to evaluate the trigonometric function to four decimal places.

A) "1.3504

B) "5.6713

C) "0.7405

D) 0.9848

E) "0.1763

Describe the level curves of the function. Sketch the level curves for the given c-values.

, c = 0, 2, 4, 6

A)

B)

C)

D)

E)

Find the indefinite integral and check your result by differentiation.

A)

B)

C)

D)

E)

Use the integration to find the general solution of the differential equation .

A)

B)

C)

D)

E)

The value for which Newton's method fails for the function below is shown in the

graph. Give the reason why the method fails.

A)

B)

C)

D)

E)

If is an exponential random variable with the probability density function

find

A)

B)

C)

D)

E) 1

The arrival time t of a bus at a bus stop is uniformly distributed between A.M.

and A.M. What is the probability that you will miss the bus if you arrive at the

bus stop at A.M.? Round your answer to two decimal places.

A) 0.25

B) 0.67

C) 0.36

D) 0.33

E) 0.57

Determine whether the function is a solution of the differential equation

.

A) Solution

B) Not a solution

How long (in years) would $400 have to be invested at an annual rate of 10%,

compounded continuously, to amount to $530?

A) 3.25 years

B) 2.95 years

C) 0.56 years

D) 4.54 years

E) 2.81 years

Use integration by parts to find the integral below.

A)

B)

C)

D)

E)

Evaluate and for the function at the point .

A) "25 and "50

B) "45 and "80

C) "25 and "80

D) 100 and "30

E) "25 and 70

Sketch the graph of the equation given below. Use intercepts, extrema, and asymptotes

as sketching aids.

A)

B)

C)

D)

E)

A power station is on one side of a river that is 0.5 mile wide, and a factory is 6.00

miles downstream on the other side of the river. It costs 18 per foot to run overland

power lines and 21 per foot to run underwater power lines. Estimate the value of x

that minimizes the cost.

A) 0.51

B) 0.83

C) 0.87

D) 1.86

E) 0.52

Find the sum of the squared errors for the linear model and the quadratic model

using the given points.

A) ;

B) ;

C) ;

D) ;

E) ;

Write an equation of the line that passes through the point (i) parallel to the given line,

and (ii) perpendicular to the given line.

A) (i) parallel: x = 3 (ii) perpendicular: y = "6

B) (i) parallel: y = "6 (ii) perpendicular: x = 3

C) (i) parallel: x = "6 (ii) perpendicular: y = 3

D) (i) parallel: x = "3 (ii) perpendicular: y = 6

E) (i) parallel: y = 6 (ii) perpendicular: x = 3

Sketch the graph of the function .

A)

B)

C)

D)

E)

Determine the convergence or divergence of the series . Use a symbolic

algebra utility to verify your result.

A) The series converges.

B) The series diverges.

Sketch the graph of the function below. Choose a scale that allows all relative extrema

and points of inflection to be identified on the graph.

A)

B)

C)

D)

E)

Write the the differential equation by separating the variables.

A)

B)

C)

D)

E)

Test the series for convergence or divergence using any appropriate test.

A) diverges

B) converges

You are in a boat 2 miles from the nearest point on the coast (see figure). You are to go

to a point Q, which is 3 miles down the coast and 1 mile inland. You can row at 8 miles

per hour and walk at 9 miles per hour. Toward what point on the coast should you row

in order to reach point Q in the least time? Round your answer to three decimal places.

A) approximately 2.286 miles

B) approximately 2.722 miles

C) approximately 1.606 miles

D) approximately 1.831 miles

E) approximately 2.486 miles

Find the derivative of the function.

A)

B)

C)

D)

E)

Find any horizontal asymptotes for the given function.

A)

B)

C)

D)

E) no horizontal asymptotes

Area. The radius, r, of a circle is increasing at a rate of 5 centimeters per minute.

Find the rate of change of area, A, when the radius is .

A)

B)

C)

D)

E)