Largest Number - Calculus - Exam, Exams of Calculus

This is the Exam of Calculus which includes Statement, Integral, Function, Graph, Right Hand Sums, Rectangles To Estimate, Definition, Derivative, Method Besides etc. Key important points are: Largest Number, Graph, Derivative, Integrate, Method, Derivative, Rolling, Snowball, Volume Increasing, Radius Increases Steadily

Typology: Exams

2012/2013

Uploaded on 02/21/2013

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Name:
Student ID:
Section:
Instructor:
Math 112 (Calculus I)
Final Exam Form A
April 14, 2012, 11:00 a.m. 2:00 p.m.
Instructions:
Work on scratch paper will not be graded.
For questions 16 to 24, show all your work in the space provided. Full credit will be given
only if the necessary work is shown justifying your answer. Please write neatly.
Should you have need for more space than is allotted to answer a question, use the back of
the page the problem is on and indicate this fact.
Simplify your answers. Expressions such as ln(1), e0, sin(π/2), etc. must be simplified for full
credit.
Calculators are not allowed.
For Instructor use only.
# Possible Earned
MC 45
16 10
17 5
18 5
19 6
Sub 71
# Possible Earned
20 6
21 6
22 6
23 5
24 6
Sub 29
Total 100
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pf5

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Name: Student ID: Section: Instructor:

Math 112 (Calculus I)

Final Exam Form A

April 14, 2012, 11:00 a.m. – 2:00 p.m.

Instructions:

  • Work on scratch paper will not be graded.
  • For questions 16 to 24, show all your work in the space provided. Full credit will be given only if the necessary work is shown justifying your answer. Please write neatly.
  • Should you have need for more space than is allotted to answer a question, use the back of the page the problem is on and indicate this fact.
  • Simplify your answers. Expressions such as ln(1), e^0 , sin(π/2), etc. must be simplified for full credit.
  • Calculators are not allowed.

For Instructor use only.

Possible Earned

MC 45

Sub 71

Possible Earned

Sub 29

Total 100

Free response: Write your answer in the space provided. Answers not placed in this space will be ignored.

  1. (10 points) Short answer. Two points each part. You do not need to show your work on this problem.

(a) Find lim x→ 2 +

x − 2

Answer:

(b) Use the given graph of f to find the largest number δ such that

if 0 < |x − 3 | < δ then |f (x) − 2 | < 0. 3.

Answer:

(c) Find the derivative of ln(x − 3).

Answer:

(d) Integrate

tan x sec x dx.

Answer:

(e) If

1

f (x) dx = 12 and

1

f (x) dx = 4, what is

4

f (x) dx?

Answer:

  1. (6 points) Suppose that a post office can accept a package for mailing only if the sum of its length and its girth (the perimeter of its cross section) is at most 120 in. What is the maximum volume of a rectangular box with square cross section that can be mailed?

x

x

y

  1. (6 points) Find the derivatives.

(a) Find f ′(x) if f (x) = 7x

2 .

(b) Find g′(x) if g(x) =

∫ (^) ln(x)

x

2 + t^3

dt.

  1. (6 points) Find the limits.

(a) lim x→ 0

tan √ x x

(b) lim n→∞

n

∑^ n

i=

2 i n

  1. (6 points) In this problem, you will analyze the curve given by

f (x) = x^4 − 8 x^3 + 18x^2 − 8 x + 5.

(a) Find all intervals where f (x) is concave up and all intervals where f (x) is concave down.

(b) At which values of x does f (x) have an inflection point?

END OF EXAM