# hw9-26 - Math 170-010 Homework 9/26 Fall 2011 Goals Compute...

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Math 170-010 Homework 9/26 Fall 2011 Goals: Compute some hard limits. Compute some hard derivatives. Note: For purposes of this homework set, you may assume as given that lim h 0 sin h h = 1 and d dx sin x = cos x Exercises: 1. Compute lim h 0 cos h - 1 h . Use a table of values something like this to guess the answer. h - 0 . 02 - 0 . 01 0 0 . 01 0 . 02 cos h - 1 h 2. Compute lim h 0 cos h - 1 h . Start with the trick cos h - 1 h · cos h + 1 cos h + 1 Later you might want a trig identity cos 2 h - 1 = - sin 2 h 3. Graph the function g ( x ) = cos x . Look at x = 0. What is g (0)? 4. For g ( x ) = cos x , compute the secant slope on [0 , h ]. What happens when h 0? 5. Compute g ( π/ 3). Suggestion: write your secant slope as cos( π/ 3 + h ) - cos( π/ 3) h Then use the trig identity: cos( a + b ) = cos a cos b - sin a sin b . 6. Compute g ( x ). Use fixed end x and free end x + h . Proceed as in Problem 5. 1

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7. Compute d dx tan x . Write it as sin x cos x and use the quotient rule. Simplify until you get sec 2 x .
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