Spring 2012
MATH 1220-002: Exam 1
Name:
___________
Robbie Sneilman
Instructions: The following questions are intended to assess your abilities on the basic concepts that we
have covered thus far. Answer all questions to the best of your ability and simplify all solutions as much as
possible. Regardless of the simplicity of the problem all work must be shown in order to receive full credit,
otherwise no credit will be awarded.
Problem 1: Compute the following:
~,
a.) Let
y
=
1n(~/3x
—
2), find
c’~
~
3
b.) Let
c.) Find
y
= 32X2_3X,
find
fx2c2dx
1~ o~X
2
I
j~ 2
S
a.) Evaluate the following definite integral
~‘
Jo
U~ Z~4~4t+~
d
~
2t2+4t+3
~t~ui~&~
~Ufri~t ço
çj JELL
~A~i;~
U
L~
(~
=
~f~’
~
~
9 b.)
Compute the following indefinite integral
r
I
J
1-k~~~
I
e~
e_l/x
Sdi~
~
dx
x2
—
~AJ~
2
~‘-~a~
C
L4Lt
(0
~ Problem 3: A radioactive substance has a half-life of 700 years. If there were 10 grams initially, how
~ much would be left after 300 years? (Recall that the formula for radioactive decay is y(t) yoe~).
~b
(0
r~
9rct~v~≤.
(~c~
So
-~
~OV
)
(0
~.i0
€
~ L~.
~
/
~to
~4)~L~Z
Z
10
3
/ ~ Problem 4: Solve the following differential equation
dy
(x + 1)— +
dx
2y
=
(x
+
1)
4
~ (~
(.~-~N ~
~°
j
—)
t
C~
(1%
~
/
—.
~i_
~‘%I)
~2~-
(
I (x.~-i~~
~
~
(‘~.
C
~x~
ha’)
Problem 5
a.) Suppose
5
h.) Let f(x)
f is a one-to-one function with f(5)
=
4. Find
f’(4) and (f(5))’.
10 + 4x + .5e~. Find f1(14 + Se).
4
co ~
~S~•
~>o
~
5e-’(
~‘*
IC FLI~t H.~t
14+SE;
5
So
a~•I ~
(L(f~))
Extra Credi~tJ) Compute the following integral
J
(Hint: Try using a property of exponents to simplify the integrand)
~
Uk ~
ttw~ cL~ ~
ue~
~
/
6