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Unformatted text preview: MATH 140 FINAL EXAM
TIME: MAY 13, 1.303.30, 2006 1. Write your name and ID #, TA and section #, question number #
and honors pledge on each of 6 answer sheets. 2. Answer each question on ONE answer sheet:
using the front for part (a) and the back for part 3. Show all your work, using complete English sentences. Cross out any
material that you do not wish graded. 4. Calculators are NOT allowgd. Good luck! 1(a) (20 pts) Compute the following (if they exist) sin(a: — 2) (1‘) 31613) cos(1/a:) (z‘z’) $13; $2 _ 4 , (m) £3100 el/w
(b) (15 pts) Use the deﬁnition of derivative (and limit rules only) to ﬁnd
ad;le at x = 0
2(a) (20 pts) Use derivative rules to differentiate
(i) f(:r) =1n(e2w+e—23), (ii) h(t) = 63‘, (m) g(s) = mliafafjis). (simplifying where possible) (b) (15 pts) A company makes rectangular crates of volume 100 ft3 with one side (and its opposite face) square. Construction costs are $ 1 / ft2
for the top, $2/ft2 for the sides and $5/ft2 for the bottom. What
dimensions minimizes the cost. CRATE % 3(a) (20 pts) For which intervals is the graph of concave down. (b) (15 pts) We deﬁne a curve by the equation
mgy + y3 = x4 + 1 Show that the tangent to the curve is never vertical. 4(a) (20 pts) Determine the number of roots in the interval 0 < m < 1 of
the equation
93: _ 1
7 + x8 _ (b) (15 pts) Use linear approximation to compute (1.002)11 5(a) (15 pts) Find the area between thecurves
f(ac) = 2x2 — e3” , 9(1): 952 —— 639” + 9
for 2 S a: g 3.
(b) (25 pts) Determine 0 t
(2') / m/‘F—xdx, (12‘) / {3t3+%e3t—3} dt, (m) %/ eszds
—3 —t 6(a) (10 pts) What type of conic section is the quadratic x2—2x—4y2—16y—8=0 (b) (10 pts) Find its vertices. ...
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This note was uploaded on 04/04/2010 for the course MATH 113 taught by Professor Staff during the Spring '08 term at Maryland.
 Spring '08
 staff
 Algebra

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