# DiferentaEam FulesCHAPTER 31203.1 EXERCISES34w1. (a) How is the number e defined?Use a calculator to estmate the walnes of the limis35.282.7 1correct to two decimal places. Whan can you conchudeabout the vallne of e?37-38 BCarve a2. (a) Sketch, by hand, the graph of the function f)paying particular attention to how the graph crosses they-axis. What fact allows youe to do this?b What types of functions are fx)= e and gx)= x?Compare the differentiation formulas for f and g(c) Which of the two functions in part (b grows more rapidlywhen x is large?37-339-40givenn the39. у3-32 Differentiate the function4. f(x) = e3. f(x) 2441-4to ex3x 126. gx) =5. f(x)= 5.2x 2.341.8. f(t) 1.4 - 25 6.77. f(t) 213- 312- 442.9. g(x) x(1 2x)10. H(u) — (Зи — 1) (и + 2)12. B(y) cy11. g(t) = 21 3/443.513. F(r)r314. y x/ -x2/34e(За + 1)?15. R(a)16. h(t)17. S(p) p px(2 + x)18. y419. y 3e20. S(R)4TT R2Vx3Xtx21. h(u) Au Bu Cu22. y2x24x + 323. у 324. G(t) 5t +Vxt25. j(x) x24e2426. k(r) = e' + rA+Bz Cz227. G(q) (1q 1)28. F(z)z229. f(v) - 2ve"1 + 16t230. D(t)V(4t)A+Be31. z=32. y ext+1==33-36 Find an equation of the tangent line to the curve at thegiven point.33. y 2x3- x2 2, (1, 3)ekRE

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I am doing Calculus HW in the James Stewart Calculus Eighth Edition and I am having problems with #29 on page 180. I am suppose to differentiate the function that is provided. help_outlineImage TranscriptioncloseDiferentaEam Fules CHAPTER 3 120 3.1 EXERCISES 34w 1. (a) How is the number e defined? Use a calculator to estmate the walnes of the limis 35. 28 2.7 1 correct to two decimal places. Whan can you conchude about the vallne of e? 37-38 B Carve a 2. (a) Sketch, by hand, the graph of the function f) paying particular attention to how the graph crosses the y-axis. What fact allows youe to do this? b What types of functions are fx)= e and gx)= x? Compare the differentiation formulas for f and g (c) Which of the two functions in part (b grows more rapidly when x is large? 37-3 39-40 given n the 39. у 3-32 Differentiate the function 4. f(x) = e 3. f(x) 24 41-4 to ex 3x 12 6. gx) = 5. f(x)= 5.2x 2.3 41. 8. f(t) 1.4 - 25 6.7 7. f(t) 213- 312- 4 42. 9. g(x) x(1 2x) 10. H(u) — (Зи — 1) (и + 2) 12. B(y) cy 11. g(t) = 21 3/4 43. 5 13. F(r) r3 14. y x/ -x2/3 4e (За + 1)? 15. R(a) 16. h(t) 17. S(p) p p x(2 + x) 18. y 4 19. y 3e 20. S(R) 4TT R2 Vx 3 Xtx 21. h(u) Au Bu Cu 22. y 2 x24x + 3 23. у 3 24. G(t) 5t + Vx t 25. j(x) x24 e24 26. k(r) = e' + r A+Bz Cz2 27. G(q) (1q 1) 28. F(z) z2 29. f(v) - 2ve" 1 + 16t2 30. D(t) V (4t) A +Be 31. z= 32. y ext+1 == 33-36 Find an equation of the tangent line to the curve at the given point. 33. y 2x3- x2 2, (1, 3) ek RE fullscreen
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Step 1

Recall the property of differentiating a rational function.

Step 2

Find the derivative of the giv... help_outlineImage TranscriptioncloseThe given function is f (v)= _Vv-2ve The derivative of the given function is as follows d 2ve" d 11 dv dv d (2ve)(-2ve) dv d d (2ve)-1(-2) dv dv --2[le" + v(e')] -+2ve Зу3 || fullscreen

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