Math 141H Homework 10 Solution (Section 8.7)
Show all your work. Jumping to the right answer without minimum reasoning deserves no credit.
1. Determine whether the following improper integrals converge. If convergent, nd the value.
3
dx
4 + x2
(1)
1
1
dx
MIDTERM EXAMINATION I, October 6, 2016
Math 131
Calculus for the Life Sciences II
Prof. G. Forni
Duration: 75 minutes
Open book, no notes, no calculators, no cell phones or electronic devices.
All problems are of equal value. Total: 100 points.
I) Compute
MIDTERM EXAMINATION III, December 1, 2016
Math 131
Calculus for the Life Sciences II
Prof. G. Forni
Duration: 75 minutes
Open book, no notes, no calculators, no cell phones or electronic devices.
All problems are of equal value. Total: 100 points.
I) Let
Math 141H Homework 1 (Section 6.1. Work) Solution
Show all your work. Jumping to the right answer without minimum reasoning deserves no credit.
1. Find the volume of the solid whose base is the region given by the ellipse 4x2 + y 2 = 1 such that
(1) each
Math 141H Homework 3 Solution (Section 6.2, 6.7 and 6.8)
Show all your work. Jumping to the right answer without minimum reasoning deserves no credit.
1. Find the length of the curve that can be represented as the graph of the function f (x) =
on the inte
Math 141H Homework 5 Solution (Section 7.1-7.3)
Show all your work. Jumping to the right answer without minimum reasoning deserves no credit.
1. Find the inverse of f (x) =
Solution:
y=
ex 1
.
ex + 1
ex 1
ey 1
1+x
= x = y
= xey + x = ey 1 = ey =
.
ex + 1
Homework 6 Solution (Section 7.5 and 7.6)
Show oil your work. Jumping to the right answer without minimum reasoning deserves no credit.
1. Compute
(1)003 (sirr1 , (2) sin (tan"1(\/E))
Soiuiion (1) Let 6 = sin1 Then, sine = Therefore,
cos (sin'1 =
Math 141H Homework 7 Solution (Section 8.1)
Show all your work. Jumping to the right answer without minimum reasoning deserves no credit.
1. Compute the integral
2
(1)
e2
x sin xdx,
1
x2 ln xdx,
(2)
0
x 2x dx
(3)
1
0
e
(ln x)2 dx,
(4)
x sec2 xdx,
(5)
(6)
Math 141H Homework 9 (Section 8.4 and 8.6) Solution
Show all your work. Jumping to the right answer without minimum reasoning deserves no credit.
1. Find the integral
(1)
x2
dx
x2 1
x2 1 + 1
1
x2
=
=1+ 2
21
21
x
x
x 1
Solution:
x2
x2
dx = x +
x2 1
=
1
1
1
MIDTERM EXAMINATION II, November 3, 2016
Math 131
Calculus for the Life Sciences II
Prof. G. Forni
Duration: 75 minutes
Open book, no notes, no calculators, no cell phones or electronic devices.
All problems are of equal value. Total: 100 points.
I) Consi