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t1sample - Math 115 001 Test 1 Sample Problems Fall 2011...

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Math 115 001 Test 1 - Sample Problems Fall 2011 Here are some sample problems to give you an idea of the type of problems that will appear on Test 1. This is not a comprehensive review. (1) Find the limits: lim x 0 x 3 - 1 x ; lim x →∞ x 3 - 2 x 2 + x - 3 x 3 + 5 x ; lim x →-∞ x 2 + 2 x + 1 5 x 4 + 10 x 2 ; lim x 0 sin x 2 x . (2) Use the definition of derivative to find the derivative of f ( x ) = x + 1. No credit if you don’t use the definition. (3) Find the derivative of the function. You don’t have to use the definition, but you must show your work. f ( x ) = x 3 ln( x 2 + 1) (4) Find the equation of the tangent line to the graph of y = 2 x - 1 x + 1 at x = 1. (5) Use limits to find all asymptotes of the function f ( x ) = 2 x 2 + 1 x 2 - 4 . You must show your reasoning based on limits. (6) Let g ( x ) = x 3 - 3 x 2 + 10. Find all critical points of g ( x ) and intervals where g ( x ) is increasing and decreasing. Find all points of inflection and intervals where it is concave up and concave down. Sketch the graph of g ( x ).
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