Spring 2003 Math 151 COMMON EXAM 1 Test Form A PRINT Last Name First Name Signature ID Instructor s Name Section INSTRUCTIONS 1 In Part 1 Problems 1 11 mark the correct choice on your ScanTron form using a 2 pencil For your own records also record your choices on your exam The ScanTrons will be collected after 1 hour they will NOT be returned 2 In Part 2 Problems 12 16 write all solutions in the space provided You may use the back of any page for scratch work but all work to be graded must be shown in the space provided CLEARLY INDICATE YOUR FINAL ANSWERS 1 Part I Multiple Choice Problems Each problem is worth 4 points No partial credit will be given Calculators may not be used on this part Scantron forms will be collected after one hour 1 Calculate lim sin x x a 0 b 1 c 1 d The limit does not exist 1 e 2 2 Find the derivative of f x 3x3 5x2 x 7 5 a x2 x 1 2 b 9x2 10x 1 3 5 1 c x4 x3 x2 7x 4 3 2 2 d 3x 5x 1 e 6x2 5x 5x2 2x 3 x 3x2 5x 2 3 Evaluate lim a b c d e 3 2 2 5 0 5 3 4 A line is given by the parametric equations x 2t 3 y 7t 2 Find the slope of this line a 7 2 b c 3 2 d e 2 7 2 7 2 3 2 5 The polynomial x3 3x 5 has only one real root In which interval does it lie a 0 x 1 b 1 x 0 c 1 x 3 d 5 x 1 e 3 x 7 x3 x x 1 x2 5x 4 6 Evaluate lim a 0 b 1 2 c 3 2 d 5 e 7 Consider the function f x x2 c x 1 2c x x 1 For what value of c is f x continuous at x 1 a c 1 2 b c 3 c c 0 1 d c 2 1 e c 3 8 Find the vertical asymptotes of y a x 1 3 b x 2 and x 2x2 5x 2 3x2 7x 2 1 3 1 2 1 d x and x 2 2 e There are no vertical asymptotes c x 3 9 Determine which vector is perpendicular to the line passing through the points 2 1 and 3 5 a h2 1i b h 1 2i c h1 4i d h 4 1i e h5 3i 10 With h x f x g x suppose f 2 1 f 0 2 3 g 2 5 and g0 2 1 Then a h0 2 3 b h0 2 16 c h0 2 8 d h0 2 4 e h x is nondifferentiable at x 2 11 With h x f x g x suppose lim f x 5 f c 3 lim g x 7 and g c 2 Then x c x c a lim h x 31 x c b lim h x 35 x c c lim h x 6 x c d lim h x 7 x c e lim h x does not exist x c 4 Part II Work Out Problems Partial credit is possible Calculators are permitted during the second hour only Show your work An answer with no work is not acceptable 12 Consider the function f x 1 2x 3 a Calculate f 0 1 using only the definition of derivative 6 points 1 b Find the equation of the line tangent to the curve y at the point 2x 3 1 1 4 points 5 13 Find parametric equations for the line passing through the points 1 2 and 5 1 8 points 5 14 Find the derivative of f x in each case 4 points each a f x 5x 2 x2 3x 1 b f x 3x3 2x2 x 7 x2 4x 3 c f x x3 x 1 15 Find lim sin x sin Justify your answer 7 points x 0 x 6 16 Consider the triangle whose vertices are 1 3 3 1 and 2 2 Choosing the segment 1 3 3 1 as the base of the triangle find the altitude 9 points y x 17 Calculate the following limits 5 points each x 2 a lim 2 x 4 x 16 b lim x x2 x 1 3x 4 7
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