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test 1- 2008 - f x = 4 x-1(b Find the slope of y = f x at x...

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Math 202-01 Exam 1 Spring 2008 Name: ID: Date: Directions: Please show all work unless specified otherwise. You may use a basic scientific calculator, but no graphing calculators. Use proper notation. Please show ID before you leave. 1. (16 pts) Using the graph of f ( x ), determine the following. Use ±∞ where appropriate. (a) lim x →- 2 - f ( x ) (b) lim x →- 2 + f ( x ) (c) lim x 0 - f ( x ) (d) lim x 0 + f ( x ) (e) lim x →- 2 - f ( x ) (f) lim x 0 + f ( x ) (g) lim x 1 f ( x ) (h) lim x 2 + f ( x ) (h) Determine where f ( x ) is discontinuous. Justify your answer. (i) Determine where f ( x ) is not differentiable. Justify your answer.
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2. (16 pts) Evaluate the following limits. Show all of your work or justify your answers! (a) lim x →- 5 x 2 + 8 x + 15 x 2 + 5 x (b) lim x 1 f ( x ) where f ( x ) = ( x 2 + 4 x if x < 1 , 3 x 3 + x + 1 if x 1 . (c) lim x + 4 x 2 + 5 x x 2 - 4 x 3. (10 pts) Determine where the following functions are discontinuous. Classify any discontinuities as holes, jumps, or vertical asymptotes. (a) f ( x ) = x 2 - 9 x - 3 (b) lim x 1 f ( x ) where f ( x ) = ( x 2 + 1 if x 1 , 2 x 2 - 1 if x > 1 .
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4. (16 pts) Let f ( x ) = 2 x 2 - x . (a) Use the definition of derivative to verify that the derivative is
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Unformatted text preview: f ( x ) = 4 x-1. (b) Find the slope of y = f ( x ) at x =-1. (c) Find the point on the graph of y = f ( x ) at x =-1. (d) Find the tangent line, in slope-intercept form, to y = f ( x ) at x =-1. 5. (12 pts) If y = 3 √ 3 x + 2, find d 3 y dx 3 . 6. (30 pts) Using the derivative rules developed in class, find the derivatives of the following. Do not simplify your answers. (a) g ( x ) = 5 x 10 + 4 4 √ x 3 + x 5-42 (b) f ( x ) = ( x 12 + 3 x 4 + 4)(4 x 3-1) (c) y = 1-2 x 2 x 4-2 x 2 + 5 (d) h ( x ) = 5 7 (2 x 3-x + 6) 14 + 3 x (e) y = 3 x 3 √ 4 x 4 + 3 Extra Credit 5 pts: For f ( x ) = ax 2 + bx + c where a,b,c are constants and a 6 = 0, find where the instantaneous rate of change is zero. What is this called?...
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