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Unformatted text preview: M4080 Fall 2009
Assignment 3 Due Thursday, September 17 You should have read and understood sections 3.3, 3.4, and 3.5 before completing
this assignment. You must show sufﬁcient work in order to receive full credit for a problem. Please
write legibly and label the problems clearly. Circle your answers when appropriate. Multiple papers must be stapled together. Write your name and the time of your
discussion section on each page. You may use calculators for arithmetic. I strongly discourage you from using a cal culator to do any algebraic simpliﬁcation, etc., since you will not be allowed to use
one on the exams. Feel free to discuss these problems with your classmates. However, each student must
write up his or her own solution. _ 2
(1 cosac) , $750
1. Let f(a:) = a:
0, cc=0 Show that f is differentiable for all 9:, and ﬁnd f’ (0) Determine whether or not f’ is
continuous at a: = 0. 2
m —4m+4, 3:21
2.Letf(x)= am+b, x<1 Find values of a and b so that f is differentiable at a: = 1. 3. Find all points on the curve y = 2 secw + tan m, for 0 S a: g 27r, where the tangent
line is horizontal. Use exact values. 4. Find the indicated derivatives. Simplify your answers to a reasonable degree. sin a: l 2
5. Let f (m) = (m) . Find the equation of the tangent line to the curve y = f (1:) when a: = g Use exact values. 1+5 ohm, KJ VAC) ‘3 W {AW )0 190,
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 Spring '06
 McAdam

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