MATH 1B FINAL (PRACTICE 1) PROFESSOR PAULIN

MATH 1B FINAL (PRACTICE 1) PROFESSOR PAULIN

DO NOT TURN OVER UNTIL INSTRUCTED TO DO SO.

CALCULATORS ARE NOT PERMITTED

THIS EXAM WILL BE ELECTRONICALLY SCANNED. MAKE

SURE YOU WRITE ALL SOLUTIONS IN THE SPACES

PROVIDED. YOU MAY WRITE SOLUTIONS ON THE BLANK

PAGE AT THE BACK BUT BE SURE TO CLEARLY LABEL

THEM

!

!

tan(x) dx = ln | sec(x)| + C

sec(x) dx = ln | sec(x) + tan(x)| + C

cos2(x) = 1 + cos(2x) 2

sin2(x) = 1 - cos(2x) 2

K(b - a)3

K(b - a)5

|EMidn |

24n2

|ESn| 180n4

ex

=

1

+

x

+

x2 2

+

x3 6

+

???

=

"

n=0

xn n!

sin x

=

x

-

x3 3!

+

x5 5!

-

x7 7!

+

x9 9!

-

?

cos x

=

1

-

x2 2!

+

x4 4!

-

x6 6!

+

x8 8!

-

? ?

? ?

?=="" n= n=0(0-(-11)n)n(x2(n2x2n+2n+n)1!1)!

arctan x

=

x

-

x3 3

+

x5 5

-

x7 7

+

x9 9

-

???

=

"

n=0

(-1)n

x2n+1 2n+1

ln(1

+ x)

=

x

-

x2 2

+

x3 3

-

x4 4

+

x5 5

-

???

=

"

n=1

(-1)n-1

xn n

#$

(1

+

x)k

=

1

+

kx

+

k(k-1) 2!

x2

+

k(k-1)(k-2) 3!

x3

+

???

=

"

n=0

k n

xn

limn(

n+1 n

)n

=

e

Name:

Student ID:

GSI's name:

Math 1B

Final (Practice 1)

This exam consists of 10 questions. Answer the questions in the spaces provided.

1. Compute the following integrals: (a) (10 points)

Solution:

! x2 ln(x3)dx

PLEASE TURN OVER

Math 1B (b) (15 points)

Solution:

Final (Practice 1), Page 2 of 12

!

x2 - 9

x4 dx

8T

81

8T

81

81

81

81

PLEASE TURN OVER

Math 1B

Final (Practice 1), Page 3 of 12

2. (25 points) Calculate the area of the surface of revolution (around the x-axis) of the curve y = (x - 1)3,

between x = 1 to x = 2.

Solution:

PLEASE TURN OVER

Math 1B

Final (Practice 1), Page 4 of 12

3. (25 points) Determine if the following series are convergent or divergent. You do not need to show your working.

(a) Solution:

% 1 (

- 1)

n+1 n

n=2

Convergent

(b) Solution:

(c) Solution:

% (-1)n cos(1/n3)

n=1

Divergent

% n + 1 n4 - 10

n=1

Convergent

(d) Solution:

% 5n 3n + 4n

n=1

Divergent

(e)

Solution:

Divergent

% nn n!

n=1

PLEASE TURN OVER

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