Answers to Third Exam (math 151 Spring 2008)


FORM A
FORM B
FORM C
1
(1/14)(x+4)^14 - (4/13)(x+4)^13+C
(1/12)(x-4)^12 + (4/11)(x-4)^11+C (-1/12)(1/25^4 - 1/6^4)
2
13^5/15 - 6^5/15
29^5/15 - 3^5/15
(1/11)(x+3)^11 - (3/10)(x+3)^10+C
3
(-1/4)ln|cos(4x)| + (1/3)tan(3x)+C
(1/4)ln|sec(4x)+tan(4x)| + (1/3)sec(3x)+C (3/2)ln|x^2-7|+C
4
(5/2)ln(x^2+9)+C
(5/2)ln|x^2-7|+C (1/4)ln|sin(4x)| - (1/3)cot(3x)+C
5
(1/6)(3+ln(x))^3+C
(1/9)(2+ln(x))^3+C (1/20)(2+ln(x))^4+C
6
(1/(4pi))sin^4(pi x)+C
(-1/(4pi))cos^4(pi x)+C (-1/(5pi))cos^5(pi x)+C
7
100/3 + 33 = 199/3
100/3 + 21 = 163/3
156
8a
8b
8c
55, 21/10
(21/10)(x-25)+55
T(24.7)=54.37=5437/100
80, 31/10
(31/10)(x-25)+80
T(25.4)=81.24=8124/100
154, 43/14
(43/14)(x-49)+154
158.3=1583/10
9
(12)/(3x-5) + (12x+1)/(6x^2+x)
   + (2x)/(x^2+1)
(3)/(3x-6)+(10x+1)/(5x^2+x)
  + (8x)/x^2+1)
(3)/(3x-6)+(10x+1)/(5x^2+x)
  + (8x)/x^2+1)
10a
10b
10c
cos^4(x)
-cos^4(x)
5cos^4(5x)-3cos^4(3x)
cos^4(x)
-cos^4(x)
5cos^4(5x)-2cos^4(2x)
csc^4(x)
-csc^4(x)
5csc^4(5x)-2csc^4(2x)
11a
11b
12 + 3ln(3)
not cont's at 0
19.5 + 3ln(4)
not cont's at 0
10+2ln(3)
not cont's at 0
12
f(x)=(-4/3)x^-3 + (2/3)x^(3/2) + 8/3
f(x)=(-4/3)x^-3 + (2/3)x^(3/2) + 16/3 f(x)=(-4/3)x^-3 + (2/3)x^(3/2) + 11/3
EC
No. Answers differ only
by the constant 9.
No. Answers differ only
by the constant 16.
No. Answers differ only
by the constant 25.