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 Za
b
1
1
tdt
(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=x1/2, x = 0, x =1
7, 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= 2x3, y =
3x1/2, x = 0, x = 1
(6) [7.4]Find the exact arc length of the curve y= 2x3
2โ1 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: Zx2cos(x)dx
(9) [8.3]Evaluate: Zcos5(x) sin3(x)dx
(10) [8.4]Evaluate: Z1
โ64 โx2dx
(11) [8.5]Evaluate: Zxโ1
(x+ 1)(x2โxโ12) dx
(12) [8.8]Evaluate: Z+โ
1
4x2
x3+ 1 dx
(13) [10.1]Determine whether the sequence converges, and if so find its limit. ๎(โ1)n(n2)
n3+ 1 ๎โ
n=1
(14) [10.2]Show that the given sequence is eventually strictly increasing or eventually
strictly decreasing. ๎(2n)!
(n+ 1)!๎โ
n=1
(15) [10.3]Determine whether the series converges and if so find its sum.
โ
X
n=1 ๎4
ฯ๎n
.
(16) [10.4]Determine whether the series converges or diverges.
โ
X
n=1
enn2.
(17) [10.5]Determine whether the series converges or diverges.
โ
X
n=1
(n!)2
(2n)!.
(18) [10.6]Determine whether the series converges absolutely, converges conditionally or
diverges.
โ
X
n=1
(โ1)n(n+ 2)
n3+ 2nโ2.
(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.
โ
X
n=1
(โ1)n(xโ1)n
en(n+ 1)
Donโt forget to check the endpoints.
1