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Problem # 35
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7. ( . ) Use Taylors Theorem to nd a. power series representation for
e=
centered at a 2 1. You may assume that f has a power series representation and you need not Show
that Rn() ~> 0. Neither do you
Math 0230
Fall 2014
Midterm Exam 2
Your name:
No calculators, no books. Show all your work (no work = no credit). Write neatly. Simplify your
answers when possible.
For each problem (except the bonus)
Midterm Exam 2
Math 0230
Fall 2014
Solutions
1. (15 points) Find an equation of the tangent line to the parametric curve x = ln t + 1, y = t2 + 2 at
the point (1, 3) without eliminating the parameter.
Substitution Rule part 2
+1
=
+1
Exercises
o
2 + 5 8 =
o
1
4
4
3
+
2
0
Suppose
8
4
4
4
tan =
4 4
4
4
sin
2
= cos 0 = 0
Integration by parts
o Liate  log, inv trig, algebra, trig, exp
sin
o
6.2 Trig integrals
2
sin , cos
2
a. cos + sin = 1
b. (cos ) = , (sin ) = cos
2 +1
c. cos
sin
d. (sin )^(2 + 1) (cos )^
Evaluate = cos 2 sin2
o = (cos 6 sin2 )(cos ) (sin )
o = (cos 2 )^2 sin 2 (si
5.5 The Substitution Rule
=
o =
o
 integrand
o
=
Ex 1: evaluate
o = sin (27x) 27
o = 27 , = 27
o = , = +
o = (27 ) +
Ex 2: evaluate
o = sin 72
72
o = 1 72 =
72
o
o
1
72
72 72 =
72
1
7
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