Exam 1 Practice Problems - Calculus | MATH 220, Exams of Calculus

Material Type: Exam; Professor: Murphy; Class: Calculus; Subject: Mathematics; University: University of Illinois - Urbana-Champaign; Term: Spring 2011;

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MATH 220 Test 1 Spring 2011
Name
(circle your TA discussion section)
.AD1, TR 1:00-1:50, Sarah Son .AD2, TR 1:00-1:50, Daniel Hockensmith
.AD4, TR 1:00-1:50, Sogol Jahanbekam .AD5, TR 2:00-2:50, Daniel Hockensmith
.AD7, TR 3:00-3:50, Ners´es Aramyan .AD8, MW 11:00-12:50, Austin Rochford
.AD9, MW 9:00-10:50, Ben Reiniger
Sit in your assigned seat (shown below).
Do not open this test booklet until I say START.
Turn off all electronic devices and put away all items except a pen/pencil and an eraser.
You must show sufficient work to justify each answer.
While the test is in progress, we will not answer questions concerning the test material.
Quit working and close this test booklet when I say STOP.
Quickly turn in your test to me or a TA and show your Student ID.
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FRONT OF ROOM 314 Altgeld Hall
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MATH 220 Test 1 Spring 2011

Name

(circle your TA discussion section)

. AD1, TR 1:00-1:50, Sarah Son. AD2, TR 1:00-1:50, Daniel Hockensmith

. AD4, TR 1:00-1:50, Sogol Jahanbekam. AD5, TR 2:00-2:50, Daniel Hockensmith

. AD7, TR 3:00-3:50, Ners´es Aramyan. AD8, MW 11:00-12:50, Austin Rochford

. AD9, MW 9:00-10:50, Ben Reiniger

• Sit in your assigned seat (shown below).

• Do not open this test booklet until I say START.

• Turn off all electronic devices and put away all items except a pen/pencil and an eraser.

• You must show sufficient work to justify each answer.

• While the test is in progress, we will not answer questions concerning the test material.

• Quit working and close this test booklet when I say STOP.

• Quickly turn in your test to me or a TA and show your Student ID.

FRONT OF ROOM – 314 Altgeld Hall

1. (10 points) Given the function f (x) =

(ln x)^3 − 6

5 , find a formula for its inverse function^ f^

− 1 (x).

2. (10 points) Find the domain of the function f (x) = ln

12 − 4 x

5. (12 points) Let f (x) =^6

x

. Use the definition of a derivative as a limit to prove that f ′(x) = −^6

x^2

Show each step in your calculation and be sure to use proper terminology in each step of your proof.

6. (10 points) Carefully sketch a graph of f (x) = 3 cos (x − π/2) on the interval [0, 2 π]. Be sure to

label the tick marks along the x-axis and y-axis so that the coordinates of important points on

your graph are clearly shown.

7. (6 points) What is the value of sin (2 tan−^1 (3))? Write your answer as either a simplified fraction

or in decimal form.

8. (7 points) Determine real numbers a and b so that the expression

6 − 4 sin^2 θ

cos^2 θ can be rewritten as

a tan^2 θ + b.

(d) x→limπ/ 2

5 sin^2 x

4 cos^2 x

(e) xlim→∞

(2x + 1)^3

6 − 5 x^3

(f) xlim→ 0

x

x^2 + 16x

Students – do not write on this page!

1 (10 points)

2 (10 points)

3 (10 points)

4 (5 points)

5 (12 points)

6 (10 points)

7 (6 points)

8 (7 points)

9a (5 points)

9b (5 points)

9c (5 points)

9d (5 points)

9e (5 points)

9f (5 points)

TOTAL (100 points)