Pre-Calc Homework Solutions 60

Pre-Calc Homework Solutions 60 - 60 Section 2.4 f x f x f x...

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Unformatted text preview: 60 Section 2.4 f x f x f x f x f(0) 0 f(3) 3 f(4) 4 f(103) 103 f ( 2) ( 2) f (1) 1 f (1) 1 e 3 3. (a) (b) 4. (a) (b) 1 e 2 e 2 0.432 8.684 ln 4 3 9. (a) lim h0 y( 2 h) h y( 2) lim h0 ( 2 h)2 h 4h h h2 ( 2)2 2 ln 4 0 3 lim h0 4 4 0.462 1 103 ln 3 100 lim h0 4h h2 h f (100) 100 ln 103 3 ln 100 lim ( 4 h0 h) 5. (a) (b) 6. (a) (b) 1 ln 1.03 0.0099 3 f (3 /4) f ( /4) f (3 /4) ( /4) x f x f x f x f ( /2) ( /2) f( ) f ( /6) ( /6) f (0) 0 f( ) ( ) 1 0 = 1 /2 3 /3 3 2 3 3 1 4 4 4 and passes through 1.273 1.654 (b) The tangent line has slope ( 2, y( 2)) ( 2, 4). y 4[x ( 2)] 4 y 4x 4 (c) The normal line has slope through ( 2, y( 2)) 0.637 1 4 1 and passes 4 ( 2, 4). f( ) 1 2 1 0 (16.5, 475), (d) y y 7. We use Q1 (10, 225), Q2 Q4 (18, 550), and P (a) Slope of PQ1: 650 225 20 10 650 375 Slope of PQ2: 20 14 650 475 slope of PQ3: 20 16.5 650 550 Slope of PQ4: 20 18 (14, 375), Q3 (20, 650). 43 46 50 50 1 [x 4 1 x 4 ( 2)] 9 2 4 [ 8, 7] by [ 1, 9] Secant PQ1 PQ2 PQ3 PQ4 Slope 43 46 50 50 10. (a) lim h0 y(1 [(1 1 h2 h) h y(1) h)2 h2 h 4(1 h 4 h)] 4h [12 3 4(1)] lim h0 lim h0 2h 2h h lim h0 h0 The appropriate units are meters per second. (b) Approximately 50 m/sec 8. We use Q1 (5, 20), Q2 (7, 38), Q3 Q4 (9.5, 72), and P (10, 80). (a) Slope of PQ1: Slope of PQ2: Slope of PQ3: Slope of PQ4: Secant PQ1 PQ2 PQ3 PQ4 80 10 80 10 80 10 80 10 20 5 38 7 56 8.5 72 9.5 lim (h 2 (8.5, 56), 2) 12 14 16 16 (b) The tangent line has slope (1, y(1)) (1, 3). y 2(x 1) 3 y 2x 1 (c) The normal line has slope through (1, y(1)) y y (d) 1 (x 2 1 x 2 2 and passes through 1 2 1 and passes 2 (1, 3). 1) 7 2 3 Slope 12 14 16 16 The appropriate units are meters per second. (b) Approximately 16 m/sec [ 6, 6] by [ 6, 2] ...
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