Practice test 2

# Practice test 2 - PRACTICE TEST 2 1 Find the limits x 4 16...

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PRACTICE TEST 2 1. Find the limits: a) 4 2 16 lim 2 x x x - - b) 3 1 lim 3 x x + - c) 1 1 lim 1 x x x - - d) 5 2 2 3 lim 1 x x x →+∞ - + e) 2 4 3 5 2 lim 4 x x x →+∞ f) 1 1 limsin x x - 2. Use the graph to find: a) ( 1 lim x f x - →- b) ( 4 lim x f x + 3. Is the function ( 29 3 2 , 1 2, 1 x x f x x x ≤ - = - - continuous at x = - 1? Explain, briefly, referring to the 3 part definition of continuity.

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4. Use the Intermediate Value Theorem to show that 4 5 0 x x - - = has a solution on [1, 2] 5. a) Find 0 tan 2 lim sin x x x [SHOW ALL WORK AND DO NOT USE L’HOPITAL’S RULE] b) List all values of x where tan x is not continuous. 6. Let ( 2 4 f x x = - a) Find the average rate of change of y with respect to x over the interval [-2, -1]. b) Find the instantaneous rate of change of y with respect to x at the point x = -2. DON’T USE THE DEFINITION. 7. A particle moves in a straight line from its initial position so that after t seconds, its distance is given by 2 4 16 s t = - .
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