Quiz #5 Math 181 Name: 7/22/21 Show all your work clearly. No Work, No Credit. 1. Given functions in polar coordinates, ( )1 22sin 2 3r and rθ= = . Sketch and then set up integrals for areas of the following: (10 pts) a) Inside r1 / outside r2 b) Inside r2 / outside r1 c) Inside both r1 and r2.
2. Determine the arc – length of the curve 32r e θ= for 0 2θ π≤ ≤ (5 pts) 3. Determine the limits of the following sequences: (8 pts)
a) { } ( )2cos 3 2 32 5n
na
n+ +
=+
b) { }2 33 2
3 5
n
nnbn
+−=
+
4. Test for convergence / divergence. If convergence, then find its sum. (12 pts)
a) 2 1
11
25
n
nn
−∞
+=∑
b) 4 3
21
4 15 3n
n nn
∞
=
+ ++∑
c) 21
28 15n n n
∞
= + +∑
5. Test for convergence / divergence of the following series: (10 pts)
a) 2
7 51
3 44 2 1n
n nn n
∞
=
+ +
+ +∑
b) ( ) 5
1
1ln 3 4n n n
∞
= +∑
c) 3 6
31
2 13 2 5n
n nn n
∞
=
+ ++ +∑
6. Determine the number of terms to ensure the approximation of the sum 321 2 1n
n
n
∞
= +∑ to be accurate
within 0.005. (5 pts)
