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Unformatted text preview: For the upcoming ﬁnal, you’ll need:
1) a blue book;
2) a stapler;
3) a picture ID.
The following instruction will be on the real ﬁnal:
Books, notes are NOT allowed except that you may bring a 3” × 5”
card. No calculators are allowed. READ the problems carefully. Put ﬁnal
answers in the boxes on this page. Put high quality work in the blue book
for all answers. At the end of exam STAPLE this page to the INSIDE
front blue cover of the blue book, so that the front side faces the white
writing pages of the blue book; staple only once at the upper left corner
(one bonus point for doing this the correct way). Math 3B Practice Problems for Final Spring 2010 The ﬁnal is on Monday, June 7, 4:00 – 7:00pm at our class room.
I will have extra oﬃce hour on 6/4 Friday, 6/7 Monday 9-11am at SH 6503.
1. Find the derivative of the function y =
2. Find the following integrals.
(a) es cos(es )ds (b)√01 (e − ex )x dx
(d) 02 t 1 + t2 dt
(c) lnx x dx
(e) sin(3x)e2x dx
(f) sin2 x cos3 xdx 5x
cos x cos(u2 )du. (g) +∞
−∞ 3 x2 +1 dx. 2 x
(h) x2 +5x−6 dx
(i) 01 x ln xdx
(j) Determine if 01 x2 −6x+5 dx is convergent or divergent.
(k) Is 1+∞ √x2 +3x3 +7x7 dx convergent or divergent?
3 3. A 1000-lb cube of ice must be lifted 50 ft, and it is melting at a rate of 2 lb
per minute. Assume that it can be lifted at a rate of one foot every minute. Find the
work needed to get the block of ice to the desired height.
4. a) Find the length of the curve
x y= √ t − 1dt 1 ≤ x ≤ 16 1 b) Find the area of the surface obtained by rotating this curve about y-axis.
5. Determine the volume of the solid obtained by rotating the region bounded by
the function f (x) = ex/3 , the lines x = 0, x = 1 and the x-axis around the line y = 4. ...
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- Fall '07