Pre-Calc Homework Solutions 111

Pre-Calc Homework Solutions 111 - Section 3.8 b 111 (b) lim...

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(b) lim x } g f ( ( x x ) ) } 5 lim x 5 lim x } ˇ x ˇ 2 w 2 w x 2 w a w 2 w } 5 lim x ! 1 § 2 § } a x § 2 2 } § 5 1 (c) lim x } g f ( ( x x ) ) } 5 lim x 5 lim x } ˇ x ˇ 2 w 2 w x 2 w a w 2 w } 5 lim x ! 1 § 2 § } a x § 2 2 } § 5 1 Section 3.8 Derivatives of Inverse Trigonometric Functions (pp. 157–163) Exploration 1 Finding a Derivative on an Inverse Graph Geometrically 1. The graph is shown at the right. It appears to be a one-to- one function [ 2 4.7, 4.7] by [ 2 3.1, 3.1] 2. f 9 ( x ) 5 5 x 4 1 2. The fact that this function is always positive enables us to conclude that f is everywhere increasing, and hence one-to-one. 3. The graph of f 2 1 is shown to the right, along with the graph of f . The graph of f 2 1 is obtained from the graph of f by reflecting it in the line y 5 x . [ 2 4.7, 4.7] by [ 2 3.1, 3.1] 4. The line L is tangent to the graph of f 2 1 at the point (2, 1). [ 2 4.7, 4.7] by [ 2 3.1, 3.1] 5. The reflection of line L is tangent to the graph of f at the point (1, 2). [ 2 4.7, 4.7] by [ 2 3.1, 3.1] 6. The reflection of line L is the tangent line to the graph of y 5 x 5 1 2 x 2 1 at the point (1, 2). The slope is } d d y x } at x
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