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161E2-S06

# 161E2-S06 - MA 161 Exam 2 Spring 2006 1 If a function f is...

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Unformatted text preview: MA 161 Exam 2 Spring 2006 1. If a function f is differentiable at a, then which is necessarily true? I. lim M exists. z—m :1: -—— a II. li_r’n f(x) exists. III. f (a) exists. A. Only I. B. Only II. C. Only III. D. Only I and III. E . All are true. 2 Ltf() {cm—2, ifoZ . e = . :c 3—cx2, ifx>2 What value(s) of c make(s) f continuous at a: : 2? —2i\/E A. c: 4 B. 0:2 5 C. 6—6 5 D. P—é‘ 1 E. =— c 6 MA 161 Exam 2 Spring 2006 3.1im 239—333—652 z—+oo w—3 A. 2 B. 3 C. O D. 00 E. —00 4. 'lim 4\$2+2\$—2\$: z——>oo A. 00 B. —00 C. O D. 1/2 E. 2/3 MA 161 Exam 2 Spring 2006 5. If 5(t) = t3 — 2t + 4 gives the position of a particle at time t, its average velocity between the times t = 1 and t = 3 is A. 11 B. 12 C. 13 D. 14 E. 15 —3\$2(2\$ + 1) — (1 ~ 11:3)(11:2 + :c) A. ~ (:1:2 + \$)2 B (1—:33)(2:c+1)+3a:2(a:2+11:) ' (\$2 + :17)2 C (1 — 11:3)(11:2 + :c) + 3332(22: + 1) ' (\$2 + :17)2 D (—31172‘)(:c2 + 117) — (1 — \$3)(2\$ + 1) ' (ac2 + :13)2 , 3:82 E‘ ’22: + 1 MA 161 Exam 2 Spring 2006 _ 2 z . d\$(:l:+\/3E)(:I: +:L') - 1 2 _— A. (mm/EM +\$)+(1+2ﬁ>(2\$+1) B. 3x2 + 2:1: + 5:1:3/2/2 + 3x1/2/2 C. 2x+ «53+ 1+ 1/(2\/Ei) 1 2 D. (\$+\/§)(1+m)+(x +:c)(2:c+1) E. None of the above. 8. . lim tan 2:1: 2 \$——>0 3:1: A. 2/3 B. 4/3 C. 7r/6 D. 00 E. 0 MA 161 _ Exam 2 Spring 2006 9. Suppose that F is a differentiable function on (—00, oo), G(:L') : F052), and G’(1) : 1. Which of the following statements must be true? I. F’(2) = 1/2 II. F’(1) = 1/2 III. F’(\/§/2) = 2 A. Only I. B. Only-II. C. Only III. D. OnIyIand III. E. It is possible that none of the statements is true. 10. The equation of the tangent line drawn to the curve xcos 7m + ycos 7ry : 0, at the point (—1,1), is A. sc+y:0 B. 7rx—y.:—1—7r C. 7rx+y=7r D. \$+y=7r E. 7ry—m=7r+1 MA 161 _ Exam 2 ' Spring 2006 11. For the three functions graphed below, which is true? A. fl! = h- 3 f” = g C. 9/] : f D. hll : E. hll : f 12. If the position of a particle at moment t is s(t) = t2 + 2“, its acceleration when t = 1 is A. 5/2 B. 3/2 c. (1n 2)/2 D. 4 + (1n 2)2 E. 2+(1n 2)2/2 ...
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161E2-S06 - MA 161 Exam 2 Spring 2006 1 If a function f is...

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