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### practice test 2

Course: EJL 4791, Fall 2009
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Word Count: 451

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101, Math Spring 2008, Practice Exam 2 1) a) State the first part of the fundamental theorem of calculus. b) Use the fundamental theorem of calculus to find the derivative of the function x4 cos( t)dt g(x) = t3/2 + 7t 4 c) Use the fundamental theorem of calculus to find the derivative of the function x h(x) = 5 (t5000 e7t )dt 3 2)Find the following limits: a) limx ( x - 7 - x) x e -1 b) limx0 ex -e-x 7x c)...

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101, Math Spring 2008, Practice Exam 2 1) a) State the first part of the fundamental theorem of calculus. b) Use the fundamental theorem of calculus to find the derivative of the function x4 cos( t)dt g(x) = t3/2 + 7t 4 c) Use the fundamental theorem of calculus to find the derivative of the function x h(x) = 5 (t5000 e7t )dt 3 2)Find the following limits: a) limx ( x - 7 - x) x e -1 b) limx0 ex -e-x 7x c) limx1 x-1 - x21 -1 d) limx0 xsin x 2 5x4 e) limx -3x-3x +7 4 +7x-2 3) Show that the function f (x) = x3 satisfies the hypotheses of the mean value theorem on the interval [0, 4]. Find all numbers c in that interval that satisfy the conclusion of the mean value theorem. 4) Find the definite integral: 2 x sec2 dx a) 2 0 4 dx b) 2 1 x 4 4dx c) x 2 ln 4 d) 0 3e 2 dx x 5) Consider the function f (x) = x2 + x + 1 on the interval I = [0, 5]. a) Using a partition of I into 5 regular subintervals, use a right-endpoint sum to compute the Riemann sum for f (x). b) Without completing part c, is this an overestimate or an underestimate of the integral? 5 c) Using the Riemann sum definition of the integral, find 0 f (x)dx. 1 dy 6) a) Find dx when y is defined implicitly by the equation 2y x2 = + sin y. b) Find the first two derivatives of y with respect to x when y is defined implicitly by the equation 2x3 - 3y 2 = 7. 7) Let f (x) = x4 + 2x3 . a) Find and classify all critical points of the graph of y = f (x). b) Where is f (x) increasing and decreasing? c) Sketch a graph of f (x). Label local extrema and inflection points. Be sure to include behavior "at infinity" and any asymptotes. 8) x2 - 3 2x - 4 2(x - 3)(x - 1) (2x - 4)2 8 (2x - 4)3 f (x) f (x) f (x) = = = Use this information to sketch a graph of x. Label local extrema and inflection points. Be sure to include behavior "at infinity" and any asymptotes. 9) A 13-foot ladder is leaning against a house when its base starts to...

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Acton School of Business - EJL - 4791
Math 101 Spring 2008 Practice Test 11) Find the derivative with respect to x. 2 a) y = x(x ) b) f (x) = (3x2 + 7x - 10)(csc(x2 ) c) g(x) = sin( 3 x) x+1 d) y = x ln( x-1 ) 1 e) v(x) = (x - x )7 x f) f (x) = sin e cos ex 2) Use the limit definition
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BAGLEY 131285 261 237 213 189 165 141 117 93 69 45 21 286 262 238 214 190 166 142 118 94 70 46 22 287 263 239 215 191 167 143 119 95 71 47 23 1 288 264 240 216 192 168 144 120 96 72 48 24 2 289 265 241 217 193 169 145 121 97 73 49 25 3 290 266 242 2
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Economics 134 MACROECONOMIC PRINCIPLESProfessor Michael Donihue Office Hours: Mondays &amp; Wednesdays 34 pm 361 Diamond ext. 5232 Tuesdays 12:30 pm Michael.Donihue@colby.edu &amp; by appointment Course Web Page: http:/www.colby.edu/economics/faculty/mrdoni