(c[3 points what is the total distance the object

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Unformatted text preview: (c) [3 points] What is the total distance the object travels in the first three seconds? ( Hint : Figure out when it changes direction.) Page 2 Math 171: Exam 2 3. Evaluate the following limits, or explain why they do not exist. (a) [6 points] lim x → 2 x- 2 √ 5 + x 2- 3 . (b) [6 points] lim x → 3- 1- x 2 3- x . (c) [6 points] lim x →-∞ √ x 2 + 1 x + 1 Page 3 Math 171: Exam 2 4. [15 points] Sketch a graph of y = ( x- 1) x 2 (2 x- 1) 2 ( x + 1) . Find and label the horizontal and vertical asymptotes and all intercepts. Page 4 Math 171: Exam 2 5. Let f ( x ) = 1 2 x- 1 . (a) [6 points] Express f ( x ) as a limit. (b) [6 points] Using the limit definition of the derivative, find f ( x ). Page 5 Math 171: Exam 2 6. Find the following derivatives. Do not simplify. (a) [7 points] Find d dx p x + (5 x 2 + 1) 100 . (b) [7 points] d dx (2 x + 1) √ x 3 x 2 + 1 . Page 6 Math 171: Exam 2 7. (a) [6 points] Give the definition of “ f ( x ) is continuous at x = c .” (b) [6 points] Explain why f ( x ) = x 3- x 2- 5 √ x + 1 has a root in the interval [0 , 3]. Page 7 Math 171: Exam 2 8. (a) [6 points] Find the tangent line to the graph of x 2 y 2- 2 = y at (1 , 2). (b) [6 points] If dy dx = x y 2 , find d 2 y dx 2 . Be sure to express your answer only in terms of x and y . Page 8...
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(c[3 points What is the total distance the object travels...

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