Pre-Calc Homework Solutions 115

Pre-Calc Homework Solutions 115 - Section 3.9 35. s 115 6....

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Unformatted text preview: Section 3.9 35. s 115 6. log4 x 15 log4 x 12 15 log4 x 12 log4 x 15 12 5 ,x 4 0 ln 3x ln (12x 2) Fold 1 s s 2 7. 3 ln x ln 8. ln 3x ln (12x 2) ln (4x 4) ln x 3 Fold 2 (x 3)(12x 2) 3x 3x ln 3x x ln 3 x 19 ln 19 ln 19 ln 19 ln 3 Fold 3 If s is the length of a side of the square, then tan tan s s s s 2 1, so 2, so tan tan 1 1 and 2. 9. 2.68 1 5t ln 5 5t 18 18 ln 5 18 ln ln 5 From Exercise 34, we have tan 1 1 tan 1 2 tan 1 3. ln 5t t ln 5 t 10. s Section 3.9 Derivatives of Exponential and Logarithmic Functions (pp. 163171) Exploration 1 Leaving Milk on the Counter 1. The temperature of the refrigerator is 42 F, the temperature of the milk at time t 0. 2. The temperature of the room is 72 F, the limit to which y tends as t increases. 3. The milk is warming up the fastest at t 0. The second derivative y 30(ln(0.98))2(0.98)t is negative, so y (the rate at which the milk is warming) is maximized at the lowest value of t. 4. We set y 55 and solve; 72 30(0.98)t (0.98)t t ln (0.98) ln 17 30 ln 18 ln 18 ln (ln 5) ln (ln 5) ln 5 1.50 3x ln 3x (x x(ln 3 1 1 2x ln 2x x ln 2 ln 3 ln 3 ln 2 ln 3 1) ln 3 ln 2) x 2.71 Section 3.9 Exercises 1. 2. 3. dy dx dy dx dy dx dy dx dy dx dy dx dy dx dy dx d (2e x) dx d 2x (e ) dx d e x dx d e 5x dx d 2x/3 e dx d e x/4 dx d (xe 2) dx d 2 x (x e ) dx 55 2e x e 2x e e d (2x) dx 17 30 17 ln 30 2e 2x e x x d dx ( x) ( 5x) t ln (0.98) 28.114 4. 17 30 5x d The milk reaches a temperature of 55 F after about 28 minutes. dy 5. dt dy dt ln dx 5e 2 2x/3 e 3 5x 5. 6. 7. 8. e 2x/3 e 30 ln (0.98) (0.98)t. At t 0.343 degrees/minute. d 2x dx 3 x 4 ln (0.98) , x/4 d dx 1 x/4 e 4 Quick Review 3.9 1. log5 8 2. 7x 3. ln (e tan x d x (e ) dx d (xe x) dx e2 ex ln 8 ln 5 x e ln 7 ) e x ln 7 tan x ln (x 2) ln x x 2 (x 2)(e x) x 2e x 4 2 (e x)(2x) xe x e ex x d [(x)(e x) (e x)(1)] 4. ln (x 2 ln (x 4) 2) ln (x 2)(x 2) x 2 9. 10. dy dx dy dx d e x dx d (x 2) e dx dx 2 ( x) e x 2 x 5. log2 (8x 5) log2 (23)x 5 log2 23x 15 3x 15 e (x ) d 2 (x ) dx 2xe (x ) 2 ...
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Fall '08 term at University of Florida.

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