Spring 08 - MAC 2311 TEST 2A SPRING 2008 A Sign your...

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Unformatted text preview: MAC 2311 TEST 2A SPRING 2008 A. Sign your scantron sheet in the white area on the back in ink. B. Write and code in the'space‘s indicated: 1) Name (last name, first initial, middle initial) 2) UF ID number 3) Discussion section number C. Under “special codes”,- code in the test ID number 2, 1. 1 e 3 4 5 ~ 6 7 8 9 O a 2 3 4 5 6 7 8 9 0 . D. At the t0p right of your answer sheet, for “Test Form Code” encode A. a B C D E E. ' This test consists of 11 five—point multiple choice questions, and two sheets (4 pages) of partial credit questions worth 25 points. The time allowed is 90 minutes. ' F. WHEN YOU ARE FINISHED: 1) Before turning in your test check for transcribing errors. Any mis- takes you leave in are there to stay. 2) You must turn in your scantron and tear off sheets to your discus— sion leader. Be prepared to show your picture ID. with a legible signature. 3) The answers. will be posted on the MACZBll homepage after the exam. 1A Problems 1 - 11 are worth 5 points each. , e‘” ifacZO 1' Hm”) z {sin(2m) ifa: < 0 a. f is continuous and differentiable-at a: = 0. b. f(cc is differentiable but not continuous at m = 0. c. f is continuous and but not differentiable at a: I: 0. d. f(a:) is neither continuous nor differentiable at a: 2: 0. e.- f’(0) = 1 ’ 2. Find the derivative of f(x) :1 (3a; + 1)2(1 .+ 93)3.. f’(a:) =‘ 3,. 18(33: + 1)(1 + a3)2 > ‘ b. (353 + 1)(1 + x,)2(15m + 9) c. (3:1: +1)(1 + m)2‘(11m + 5) d. 6(339 + 1)(1 + cc)2 e. (1833 + 20)(1 + m)2 3- Given f(5) = 2, H2) = 1/3, H5) = 1/2,‘g(5) = 4, g'(2) = 1/5, f(2) = 2, and g'(,5) = ./4, then for h(a:) = g(f(a:)), find h’(5) = . 11-2— Ja 1.4 a. b. c. d. e. H gird Ooh-4 4.. The graph of y 2: has horizontal tangent line(s) at ., (w+2)'3‘ ‘ a. a: = —6 only b. 3:: +2 andez --6 0.11: = V—Z and LL": 4-S- d. there are no horizontal tangents e. a: =; ———g— only 6. Find the equation of the tangent line to :2 6(‘ws‘“1) at a: = 3. a. y = 12:33 —— 1 b. y = 3:1: —— 8 c. y = %m _ d. y 2 £33 —- 36 + 1 e. y=3em-96+1 5(t) .2 t + 9% for t > 0. If v(t) is the velocity function which of the following are true? (1) 3(t) is always increasing (2) v(t) has a horizontal asymptote (3) v(t) has a horizontal tangent line a. only (3) b. all are true (3. only (1) and d. only (2) and (3) e. only (2) 8. Find f”(:):) if f(a3) 2 see a: a. 2 sec3 :1: + sec as b. sec m tanza: + see3 a: c. cs0 cc cot a: d. —— see as e. sec3 tan a: 10. Find the slope of the tangent line to the curve y : sin(y -- :13) at (71', 0). a. 1 b. c. 0 d. ——1 e. does not exist 11. What is the maximum height reached by an object (Calculus book) which is thrown upward at a velocity of 48 ft / sec from the top of a 156'ft building (Beaty ToWers)? a. 172 it b. 165 ft c. 192 a (1. 204% e. 228 ft MAC 2311 EXAM 1 Part 11 Spring 2008 Section Number Name UF ID Number Signature SHOW ALL WORK TO RECEIVE FULL CREDIT 1. (5 points) Using the definition of the derivative find 1" Where __:c+1 “33—1 f (w) Use’the Quotient Rule to check your work. 2.‘ (5 points) Use logarithmic differentiation to compute the derivative of y = («MY 3. (5 points) Evaluate these limits. (a) limméo sifim 4. (10 points) Find 5.3;. (a) y = tan"1(e””) (b) y = 3"’2+””+.]L (C) y = ecos(ln:1:) (d) y = 1n(| sin—1(m)|) (e) e” tanm = 1 ...
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