# ERSS - f x for f x = 5 x 2-7 x 2 Recall f x = lim h → f x...

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MATH 102 - Exam 1 - 2/8/2012 Name: Section Number: Directions: You must show all work to receive full credit. You have ﬁfty (50) minutes to complete this exam. You may use a non-graphing calculator on this exam. No cell phones or iPods may be used. 1. (6 Points Each) Find the following limits: (a) lim x 6 2 x + 1 x - 3 (b) lim x →∞ ± 3 8 + 3 x - 6 x 2 ² (c) lim x 1 ± x 2 + x - 2 x 2 + 2 x - 3 ² 1

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(d) lim x 0 1 x +3 - 1 3 x 2. (6 Points) Given the graph of f ( x ), compute each of the following. # (a) lim x 1 - f ( x ) = (b) lim x 1 + f ( x ) = (c) lim x 1 f ( x ) = 2
3. For each of the following, determine the value(s) of x where the given function is discontinuous. For each, identify which condition of continuity is not satisﬁed. (a) (4 Points) f ( x ) = 7 - 3 x (1 - x )(3 + x ) (b) (6 Points) f ( x ) = 1 - x if x < 1 2 if 1 x 2 4 - x if x > 2 4. (10 Points) Find an equation of the line tangent to the graph of f ( x ) = 6 x - 2 at x = 3. 3

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5. (10 Points) Use the deﬁnition of the derivative to ﬁnd

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Unformatted text preview: f ( x ) for f ( x ) = 5 x 2-7 x + 2. Recall: f ( x ) = lim h → f ( x + h )-f ( x ) h 6. (7 Points Each) Find the derivatives for the following functions. Do not simplify your answers. (a) g ( w ) = 5 w 4 + 5 3 √ w 4 (b) y = ( 3 x-4 + 9 x-7 + 7 )( 6 x 2-8 x ) 4 (c) y = 2 e 4 x-ln (3 x-1) (d) g ( x ) = 2 e x ln x x 5 7. A company producing computer components has established that, on average, a new employee can assemble N ( t ) components per day after t days of on-the-job training, as given by N ( t ) = 40 t t + 2 (a) (6 Points) Find the average rate of change of N ( t ) from 3 to 6 days. (b) (6 Points) Find the instantaneous rate of change of N ( t ) at 3 days. 6...
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ERSS - f x for f x = 5 x 2-7 x 2 Recall f x = lim h → f x...

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