Solutions for Quiz #1
Math 221
Instructions. Be sure to show your work and explain your reasoning for full credit.
Solutions
1. Determine the point in the plane R2 where the line with slope 2 and y-intercept 1
intersects the line passing through the point
Solutions for Quiz #2
Math 221
Instructions. Be sure to show your work and explain your reasoning for full credit.
1. Compute the limit
(2 + h)2 4
lim
h0
h
Solution:
(2 + h)2 4
4 + h2 + 4h 4
h2 + 4h
h(4 + h)
= lim
= lim
= lim
= 4.
h0
h0
h0
h0
h
h
h
h
lim
Solutions for Quiz #3
Math 221
Instructions. Be sure to show your work and explain your reasoning for full credit.
1. Determine the horizontal and vertical asymptotes to
3ex + 4
2ex 1
Solution: For the horizontal asymptotes,
ex (3 + 4ex )
3
3ex + 4
3ex +
The following are the questions used for a version of Exam I in Math 221 section
AL1 in Fall 2012 (McCarthys section). It may be rather dierent than the one to be
used in sections AL1 and BL1 for Fall 2013 but it is being provided for those curious
about
Math 221/AL1 Exam I
UIUC, September 27, 2013
Instructions. Please provide your answers in the space providedusing the back of
sheets if necessary. No calculators, electronics, friends or psychic readings are to be
used while taking this test. If you are u
Quiz #5
Math 221
Instructions. Be sure to show your work and explain your reasoning for full credit.
NAME
Find the derivative
dy
.
dx
1. y = sin1 (x3 )
Solution:
1
dy
=
3x2 .
6
dx
1x
2. y = ln(tan(ex )
Solution:
dy
1
=
sec2 (ex )ex .
dx
tan(ex )
3. y = xc
The following are the questions used for the rst Exam in Math 221 section EL1
in Fall 2011 (McCarthys section). It is rather dierent than the one to be used in
sections AL1 and BL1 for Fall 2012 but it is being provided for those curious about
McCarthys e
Quiz #6 for Math 221
Instructions. Be sure to show your work and explain your reasoning for full credit.
1. A 160 F cup of coee is taken outside on a cool day of 55 F. After 10 minutes the
coee has cooled to 150 F. When will the coee cool to 110 F?
Soluti