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Test_1_Study_Guide

Test_1_Study_Guide - Test#1 Study Guide Note The following...

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Test #1 Study Guide Note: The following are sample problemes only. The real exam may differ in amount and style. 1. Find the instantaneous rate of change of the function 1 ) ( + = x x f at 2 = x . 2. A curve is given by x x f = ) ( , find: (a) the slope of the tangent at 1 = x , (b) the equation of this tangent line. 3. Evaluate the limits of the following functions: (a) 2 4 lim 4 - - x x x (b) 4 4 12 lim 2 2 2 - - + t t t (c) 2 1 lim ) 2 ( + + - - x x x (d) x x csc lim + π 4. Recall that ) ( lim x f a x exists if and only if the two limits , ) ( lim x f a x - ) ( lim x x f a + equal and exist. a. For - - = 4 6 4 4 2 ) ( x if x x if x x f , check whether ) ( lim 4 x f x exists or not. b. For x x x f = ) ( , check whether ) ( lim 0 x f x exists or not. 5. Recall that 1 sin lim 0 = x x x . Use this fact to find these limits: (a) x x x tan lim 0 (b) x x x 2 ) 3 sin( lim 0 (c) 1 ) 1 sin( lim 1 - - x x x (d) ) 5 tan( ) 3 tan( lim 0 x x x 6. Recall that 1 sin 1 - θ . Use squeeze theorem to show 0 1 sin lim 0 = x x x .

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Test_1_Study_Guide - Test#1 Study Guide Note The following...

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