
Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
A math quiz consisting of 20 problems for a calculus 142 class. The problems cover various topics such as the fundamental theorem of calculus, volume of solids of revolution, arc length, and integration. Students are required to find exact answers and show their work.
Typology: Quizzes
1 / 1
This page cannot be seen from the preview
Don't miss anything!
Math 142, Quiz 12 Name: Student #: Be neat and show your work in all problems. Circle your answers.
(1) [6.6]State the Fundamental Theorem of Calculus (Part 1). (2) [6.8]Everyone completed this one!!
(3) [6.9]Assuming ln(a) = 3 and ln(b) = 10 evaluate
โซ ab
1
t
dt (4) [7.2]Find the volume of the solid that results when the region enclosed by the given curves is revolved around the x-axis. y = x^1 /^2 , x = 0, x = 17 , y = 0 (5) [7.3]Use the cylindrical shell method to find the volume of the solid that results when the region enclosed by the given curves is revolved around the y-axis. y = 2x^3 , y = 3 x^1 /^2 , x = 0, x = 1 (6) [7.4]Find the exact arc length of the curve y = 2x
(^32) โ 1 from x = 0 to x = 1. (7) [7.6]Find the average value of g(x) = cos(x) on [0, ฯ]. (8) [8.2]Evaluate:
x^2 cos(x) dx
(9) [8.3]Evaluate:
cos^5 (x) sin^3 (x) dx
(10) [8.4]Evaluate:
64 โ x^2
dx
(11) [8.5]Evaluate:
x โ 1 (x + 1)(x^2 โ x โ 12)
dx
(12) [8.8]Evaluate:
1
4 x^2 x^3 + 1
dx
(13) [10.1]Determine whether the sequence converges, and if so find its limit.
(โ1)n(n^2 ) n^3 + 1
n= (14) [10.2]Show that the given sequence is eventually strictly increasing or eventually strictly decreasing.
(2n)! (n + 1)!
n= (15) [10.3]Determine whether the series converges and if so find its sum.
n=
ฯ
)n .
(16) [10.4]Determine whether the series converges or diverges.
n=
enn^2.
(17) [10.5]Determine whether the series converges or diverges.
n=
(n!)^2 (2n)!
(18) [10.6]Determine whether the series converges absolutely, converges conditionally or
diverges.
n=
(โ1)n(n + 2) n^3 + 2n โ 2
(19) [10.7]Find the first 4 terms of the Taylor series of sin(x) at x = ฯ.
(20) [10.8]Find the interval of convergence of the following power series.
n=
(โ1)n(x โ 1)n en(n + 1) Donโt forget to check the endpoints. 1