Math 50, Fall 2009, Final Review Sheet
The nal exam for Math 50 will take place on Friday, December 18, from 3:30 to 5:30 p.m.
in Anderson 206. To prepare the exam, do the following problems thoroughly, and leave it
there.
1. [linear approximations and Ta
Homework due on Tuesday, October 27
Trigonometric integrals: Section 7.2, problems 1, 12, 66.
Integrals involving inverse trigonometric and hyperbolic functions: Here are
three facts that will be useful in doing the integration problems given below:
1
d
a
Introduction to innite series
Innite series are innite sums:
a1 + a2 + a3 + a4 + . = ai =?
i=1
When you cut it off after n terms, you get what is called the n-th partial sum:
n
sn = ai .
i=1
We say that the series converges if the limit of sn as n exists,
Math 50, Fall 2009, Final Review Sheet, Solutions
The nal exam for Math 50 will take place on Friday, December 18, from 3:30 to 5:30 p.m.
in Anderson 206. To prepare the exam, do the review problems thoroughly, and leave it
there.
1. (a) The linear approx
Due: Tuesday, December 8
1. The four-leaved rose is given by
r = cos(2), 0 2.
Express the length of this curve as an integral. (Do not evaluate the integral. It cannot be evaluated
by nding an anti-derivative. Of course it could be evaluated using, for in
problem 14 on page 441: Initially, the chain lies on the ground. At the end, a 6 m segment
of the chain is raised up. The assumption here is that the raised segment is precisely vertical.
(The problem would become very much harder if we assumed that the r
Math 50, Fall 2009, review for rst midterm exam
The exam will take place on Friday, October 16, in our usual classroom. You will not be
allowed to use notes, books, or calculators.
1. Suppose that you know g(2) = 3 and g (x) = x2 + 12 for all x (a) Use a
Math 50, fall 2009, review for second midterm exam, solutions
The exam will take place on Friday, November 13, in our usual classroom. You will not be
allowed to use notes, books, or calculators.
1. (a) Substitute u = sin x, du = cos xdx:
(a)
Z
cos x
dx =
Math 50, fall 2009, review for second midterm exam
The exam will take place on Friday, November 13, in our usual classroom. You will not be
allowed to use notes, books, or calculators.
1. You are given the following information:
arcsin (x) =
1
1 x2
, arc
Math 50, Fall 2009, review for rst midterm exam, solutions
1. (a) g(1.95) g(2) g (2) 0.05 = 3 4 0.05 = 3.2 (b) g (x) is an increasing
function, so the graph of g is concave-up, so the linear approximation is too small.
2. g (x) = 1/x, so g(1) = 0, g (1) =