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Calculus Practice Midterm Exam 2: logarithmic differentiation |, Exams of Mathematics

Kent State University (KSU) - Ashtabula CampusMathematics

Typology: Exams

2019/2020

Uploaded on 06/15/2020

jeny
jeny 🇺🇸

4.6

(14)

251 documents

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Jim Lambers
Math 2B
Fall Quarter 2004-05
Pratie Midterm Exam 2 (Version D)
1.
Compute the average value of the funtion
f
(
x
) =
xe
x
2
over the interval [0
;
1℄.
2.
Given that the funtion
f
(
x
) =
x
2
+ 2
x
+ sin
x
is one-to-one on the domain [0
;
1
), ompute
(
f
1
)
0
(3).
1
pf3
pf4
pf5

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Jim Lamb ers Math 2B Fall Quarter 2004- Pra ti e Midterm Exam 2 (Version D)

  1. Compute the average value of the fun tion f (x) = xex

over the interval [0; 1℄.

  1. Given that the fun tion f (x) = x^2 + 2 x + sin  x is one-to-one on the domain [0; 1 ), ompute

(f ^1 )^0 (3).

  1. Given

y =

p 1 x^2 )sin

(^1) x

(2x^ )log^2 x^

use logarithmi di erentiation to ompute y 0.

  1. Evaluate the inde nite integral Z 2 tan^

(^1) x

1 + x^2

dx:

  1. Evaluate the inde nite integral (^) Z x 1 + x^4

dx:

  1. Compute the limit

lim x! 0

ln(x + 1)

x

  1. Compute the volume of the solid obtained by revolving the region b ounded by the lines

y = x^2 , y = 1, and x = 0 around the line y = 2.