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Pre-Calc Homework Solutions 62

Pre-Calc Homework Solutions 62 - 62 Section 2.4(b The slope...

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17. continued lim h 0 1 } f (2 1 h h ) 2 f (2) } 5 lim h 0 1 5 lim h 0 1 } [4 2 (2 4 1 h h )] 2 2 } 5 lim h 0 1 } 2 4 h h } 52 } 1 4 } Yes. The slope is 2 } 1 4 } . 18. No. The function is discontinuous at x 5 } 3 4 p } because lim x (3 p /4) 2 f ( x ) 5 lim x (3 p /4) 2 sin x 5 sin } 3 4 p } 5 } ˇ 2 2 w } but f 1 } 3 4 p } 2 5 cos } 3 4 p } 5 2 } ˇ 2 2 w } . 19. (a) lim h 0 } f ( a 1 h h ) 2 f ( a ) } 5 lim h 0 5 lim h 0 5 lim h 0 } 2 ah 1 h h 2 } 5 lim h 0 (2 a 1 h ) 5 2 a (b) The slope of the tangent steadily increases as a increases. 20. (a) lim h 0 } f ( a 1 h h ) 2 f ( a ) } 5 lim h 0 5 lim h 0 } 2 a a 2 h ( a 2( 1 a 1 h ) h ) } 5 lim h 0 } a ( a 2 1 2 h ) } 5 2 } a 2 2 } (b) The slope of the tangent is always negative. The tangents are very steep near x 5 0 and nearly horizontal as a moves away from the origin. 21. (a) lim h 0 } f ( a 1 h h ) 2 f ( a ) } 5 lim h 0 5 lim h 0 5 lim h 0 2 5 2 } ( a 2 1 1) 2 } (b) The slope of the tangent is always negative. The tangents are very steep near x 5 1 and nearly horizontal as a moves away from the origin.
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