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Test 1-2005

# Test 1-2005 - x = 1 4(4 pts Given the following table...

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Math 202-3 Exam 1 Summer 2005 Name: ID: Date: Directions: Please show all work unless specified otherwise. Basic calculators are okay, but no graphing calculators. Please show ID before you leave. 1. (13 pts) Using the given picture, determine the following. Note the the function has a vertical slope at x = 1. Assume the function is smooth at x = 2. -4 -3 -2 -1 1 2 3 4 -8 -6 -4 -2 2 4 6 8 (a) lim x 0 - f ( x ) = (b) lim x 0 + f ( x ) = (c) lim x 0 f ( x ) = (d) lim x 1 f ( x ) = (e) lim x 2 f ( x ) = (f) f (0) = (g) f (2) = (h) Determine the points of discontinuity of f ( x ). Justify your answers. (i) Determine where f ( x ) is not differentiable. Justify your answers.

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2. (15 pts) Evaluate the following limits. (a) lim x →- 7 ( x + 7)( x + 5) ( x + 7)( x - 1) (b) lim x →-∞ 3 - 4 x - 10 x 3 5 x 3 - 8 x + 1 (c) lim x 1 x - 2 x 2 - 2 x 3. (10 pts) Use the limit definition of derivative (yes, the long way) to find the derivative of y = f ( x ) = 4 x 2 - 5 x . No credit will be given if the limit definition of derivative is not used. Note that the answer is dy dx = 8 x - 5. Then find the equation of the tangent line at
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Unformatted text preview: x = 1. 4. (4 pts) Given the following table, estimate to the nearest integer the instantaneous rate of change and the slope of the tangent line of y = f ( x ) = 16 x 2 . h-0.1-0.01-0.001 → ← 0.001 0.01 0.1 f (1 + h )-f (1) h 30.4 31.84 31.984 → ? ← 32.016 32.16 33.6 5. (10 pts) Using the derivative rules developed in class, ﬁnd the derivatives of the following. Do not simplify your answers. (a) f ( x ) = 5 x 4 4-2 x 2 + 3 √ x-2 (b) h ( q ) = 4 q 3 + 7 q-4 q 6. (8 pts) A manufacturer produces Cougar memorabilia. If the average-cost function for this product is c = 10 q 2-2 q + 5-500 q , ﬁnd the marginal-cost function. Then evaluate it when q = 5. Extra Credit 5 pts Given y = f ( x ), what is the diﬀerence between lim x → c f ( x ) and f ( c )?...
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Test 1-2005 - x = 1 4(4 pts Given the following table...

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