Description

Don't use plagiarized sources. Get Your Custom Essay on

MATH 34 Texas University Business Calculus Questions

Just from $13/Page

Math 34 Practice Exam #1

Due on date of Exam #1

Name___________________________________ Section: _________________

Please answer each of the following questions completely. Simplify all answers. Assume answers are to be exact, unless otherwise

specified. Each question is worth 1 point and is graded on accuracy, effort, and neatness. Please show all work directly in the booklet.

Copying answers out of the key will receive no credit.

**FOR INSTRUCTOR USE ONLY – DO NOT WRITE IN THE BOXED AREAS**

Neatness: __________/10

Completeness: ________/40

Problem#______: _________/25

Problem#______: _________/25

GRADE: ____________/100

Decide whether the limit exists. If it exists, find its value.

1) Find lim f(x) and lim f(x).

x (-1)x (-1)+

Graph the function and then find the specified limit. When necessary, state that the limit does not exist.

1

2)

4×2 ,

for x -1,

f(x) = 4,

for -1 1.

Find the limit, if it exists.

x2 – 4

3) lim

x -2 x – 2

2

4) lim

x >3

x-8

Provide an appropriate response.

5) Is the function given by f(x) =

1

,

x-3

for x > 3

continuous at x = 3? Why or why not?

x2 + 5x, for x 3

Find a simplified difference quotient for the function.

6) f(x) = 2×3

Find an equation for the line tangent to the graph of the given function at the indicated point.

40

at (1, 40)

7) f(x) =

x

3

List the x-values in the graph at which the function is not differentiable.

8)

Find the derivative.

5

9) y = x4

Find all values of x (if any) where the tangent line to the graph of the function is horizontal.

10) y = x3 + 8×2 – 204x + 34

For the given function, find the points on the graph at which the tangent line has slope 1.

1

11) y = x3 – 6×2 + x

3

4

Differentiate. Use the product law. Do not simplify your final answer.

5

12) f(x) = x + (x2 – 6)

x

[Do not use algebra before differentiating]

Differentiate. Simplify. Leave the denominator in factored form.

x2 + 2x – 2

13) y =

x2 – 2x + 2

Find an expression for dy/dx.

4

and u = 7x – 5

14) y =

u2

5

Differentiate.

15) f(x) = (3 – 8x)250

Calculate the requested derivative from the given information.

16) Given f(u) = u2 and g(x) = u = x5 + 2, find (f g)'(1).

Find the indicated derivative of the function.

d3 y

x

of y =

17)

3

x

+1

dx

6

Solve the problem.

18) A company’s total cost, in millions of dollars, is given by C(t) = 220 – 60e-t where t = time in years. Find the

marginal cost when t = 4.

Differentiate.

19) y =

Solve.

4ex

2ex + 1

20) Find the equation of the line tangent to the graph of y = (x2 – x) ln (6x) at x = 2 . Approximate to the nearest

thousandth.

7

Solve the problem.

21) Suppose that P0 is invested in a savings account in which interest is compounded continuously at 5.4% per

year. That is, the balance P grows at the rate given by

dP

= 0.054P. Suppose that $6000 is invested. What is the

dt

balance after 3 years?

22) Find the tripling time for an amount invested at a growth rate 7% per year compounded continuously.

23) An artifact is discovered at a certain site. If it has 56% of the carbon-14 it originally contained, what is the

approximate age of the artifact to the nearest year? (carbon-14 decays at the rate of 0.0125% annually.)

8

24) Find the present value of $26,000 due 17 years later at 6.5%, compounded continuously.

Differentiate.

25) y = 5 6x

9

Answer Key

Testname: PRACTICE TEST 1

1) -2; -7

ID: CWAEX2B 1.1.1-1

Objective: (1.1) Find Limit Using Graph

2)

lim f(x) = 4

x -1 –

ID: CWAEX2B 1.1.3-8+

Objective: (1.1) Graph Function and Find Limit

3) 0

ID: CWAEX2B 1.2.1-7+

Objective: (1.2) Use Rational Function Limit Theorem

4) Does not exist

ID: CWAEX2B 1.2.3-3

Objective: (1.2) Find Limit of Radical Expression

5) No, lim f(x) does not exist

x 3

ID: CWAEX2B 1.2.8-8

Objective: (1.2) Determine Continuity at Point Given Function

6) 6×2 + 6xh + 2h 2

ID: CWAEX2B 1.3.1-3+

Objective: (1.3) Find Simplified Difference Quotient

7) y = – 40x + 80

ID: CWAEX2B 1.4.3-4

Objective: (1.4) Find Equation of Tangent Line

8) x = 2

ID: CWAEX2B 1.4.4-6

Objective: (1.4) Determine Differentiability from Graph

9)

dy

=

dx

5

4

5

x

ID: CWAEX2B 1.5.2-3+

Objective: (1.5) Find Derivative Using Power/Sum/Diff Rules II

10) –

34

,6

3

ID: CWAEX2B 1.5.5-8+

Objective: (1.5) Use Function to Find Points with Horizontal Tangent

10

Answer Key

Testname: PRACTICE TEST 1

11) (0, 0) and (12, -276)

ID: CWAEX2B 1.5.6-6

Objective: (1.5) Find Points at Which Tangent Has Given Slope

12) f'(x) = 2x x +

5

5

(x2 – 6)

+ 1x

x2

ID: CWAEX2B 1.6.2-5+

Objective: (1.6) Find Derivative of Product II

13)

dy

-4×2 + 8x

=

dx (x2 – 2x + 2)2

ID: CWAEX2B 1.6.4-2+

Objective: (1.6) Find Derivative of Quotient II

14) –

56

(7x – 5)3

ID: CWAEX2B 1.7.4-2+

Objective: (1.7) Find dy/dx Given y = f(u) and u = g(x)

15) f'(x) = -2000(3 – 8x)249

ID: CWAEX2B 1.7.1-3+

Objective: (1.7) Differentiate Using Extended Power Rule I

16) 30

ID: CWAEX2B 1.7.8-1+

Objective: (1.7) Find Derivative at Point Using Chain Rule

17) 6(x + 1)-4

ID: CWAEX2B 1.8.2-6+

Objective: (1.8) Find Higher-Order Derivative

18) 1.1 million dollars per year

ID: CWAEX2B 2.1.8-2+

Objective: (2.1) Solve Apps: Exponential and Logarithmic Functions of the Natural Base, e

19)

4ex

(2ex + 1)2

ID: CWAEX2B 2.2.2-4+

Objective: (2.2) Differentiate Exponential Function II

20) y = 8.455x – 11.94

ID: CWAEX2B 2.3.2-1+

Objective: (2.3) Find Eqn of Line Tangent To Graph at Given Point

21) $7055.16

ID: CWAEX2B 2.4.2-6+

Objective: (2.4) Solve Apps: Business (Exponential Model)

22) 15.7 years

ID: CWAEX2B 2.4.3-5+

Objective: (2.4) Solve Apps: Effective Annual Yield, Doubling Time

23) 4639 years

ID: CWAEX2B 2.5.1-8

Objective: (2.5) Solve Apps: Radioactive Decay

24) $8611.48

ID: CWAEX2B 2.5.3-2+

Objective: (2.5) Solve Apps: Business

11

Answer Key

Testname: PRACTICE TEST 1

25) 6 · (ln 5) · 5 6x

ID: CWAEX2B 2.6.1-3

Objective: (2.6) Differentiate General Exponential Function

12

Purchase answer to see full

attachment