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Unformatted text preview: MATH 221 LEC 1 YOUR NAME: “H Instructor: Professor Uhlenbrock CIRCLE your TA’S name:
Paul Jenkins J unwu Tu Michael Woodbury Luanlei Zhao Second Midterm Exam: Thursday November 10, 2005 Do all problems and show all your work. Answers without written steps or reasons are
worth much less than answers with correct steps and reasons. Unless otherwise indicated
you should derive exact solutions to the problems, rather than numerical approximations. You can only get credit for what you write down, not for what you might have meant by a
vague answer. Write neatly and diSplay your ﬁnal answers clearly on the lines provided with the problems.
Use the last page for scrap paper. ll MATH 221 LEC 1 SECOND EXAM THU NOV 10 PROBLEM I Part (a) { 5 points ) Approximate \5/ 32.4 using a suitable differential.
Show your work carrying at least 6 decimal digits. A mere calculator answer will receive zero credit. ANSWER:
EM Part (b) ( 5 points ) Use a suitable differential to approximate tan (ﬂ) .
Show your work carrying at least 6 decimal digits.
A mere calculator answer will receive zero credit. ANSWER:
m MATH 221 LEC 1 SECOND EXAM THU NOV 10 PROBLEM 2 ( 10 points) A farmer has 750 ft of fencing material available. She wants to fence in a
rectangular area and also subdivide the area into four pens by using fencing parallel to one
side of the rectangle. fencing material. ANSWER:
RN MATH 221 LEC 1 SECOND EXAM THU NOV 10 PROBLEM 3
Let me) = 993 :23 Part (a) ( 3’ points ) Where is f(a:) increasing and decreasing? What are the local
maximum and minimum values? ANSWER:
a Part (b) (4 points) Where is f(x) concave up and concave down? Find all points of
inﬂection. ‘ ANSWER: HE Part (c) ( 4 points ) Sketch the graph of y = f Find all vertical and horizontal
asymptotes. MATH 221 LEC 1 SECOND EXAM THU NOV 10 (10 points) Compute
7r/6 
/ $1n36 d6.
0 cos 6 PROBLEM 4 ANSWER: MATH 221 LEC 1 SECOND EXAM THU NOV 10
Part (a) { 8 points ) Find the general solution of PROBLEM 5 —:y3(x5+$). ANSWER:
Part (a) (2 points ) Find the particular solution of the above equation which satisﬁes
3/ = 7 when x 2: 0. ANSWER: MATH 221 LEC 1 SECOND EXAM THU NOV 10
Compute the integral PROBLEM 6 /01 (11:2  23) d3: using'the deﬁnition of a deﬁnite integral: Part (a) ( 8 points ) For an integer n > 1 write down and compute R n, the Riemann
sum for this integral using the regular partition of the interv a1 and right endpoint sample ANSWER: Part (b) ( 2 points ) Use the expression for Rn found in part (a) to compute the limit
lim,H00 Rn . ANSWER: MATH 221 LEC 1 SECOND EXAM THU NOV 10
Part (a) ( 5 points ) Compute PROBLEM 7 d 1 a m 026111}. ANSWER:
. ' Ma
Part (b) ( 5 paints ) Compute ANSWER: MATH 221 LEC l SECOND EXAM THU NOV 10
Part (a) (5poz'nts PROBLEM 8
) State the precise form of the Mean Value Theorem for Derivatives. AN SWER Part (b) (5 points) Determine if f(x) 2
Theorem 0n the interval [1,3]
guaranteed by the theorem. is satisﬁes the conditions of the Mean Value
and explain why or Why not; if so, ﬁnd the values of all c ANSWER: MATH 221 LEC 1 SECOND EXAM THU NOV 10
Part (a) ( 5 points ) Compute PROBLEM 9 /\3/2x—4dx ANSWER:
EN
Part (b) ( 5 pomts ) Compute 177/3 (3:3 + a: — sin(a:)) d2: 77/3 ANSWER: ...
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 Summer '07
 Denissou
 Calculus, Geometry, Derivative, Convex function, Concave function

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