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sin x 16. f(x) = 1- cos x

sin x 16. f(x) = 1- cos x

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question 16

PROBLEM SET 3.4 Level 1 DRILL PROBLEMS Level 2 APPLIED AND THEORY PROBLEMS Differentiate the functions given in Problems 1 to 20. 29. Consider three areas as shown in Figure 3.22. 1. f(x) = sin x + cos x 2. g(x) = 2 sin x + tan x 1 3. y = sin 2x sin h h 4. y = cos 2x cos h IT 5. f(t) = t2 + cos t + cos 4 JT 6. g(t) = 2 sec t +3 tant – tan 3 - 7. y = e-* sin x 8. y = tan x2 tan h 9. f(0) = sin? e 10. g(0) = cos² 0 11. y = cos x'01 = (cos x)101 13. p(t) = (t² + 2) sin t 1 = COS 12. y Figure 3.22 Triangles and a unit circle with subtended angle h. a. What is the area g(h) of the blue-shaded triangle? 14. у — х sec x b. What is the area f(h) of the pink-shaded sector? sin t 15. q(t) Hint: The area of a sector of a circle of radius r and central angle 0 measured in radians is sin x 16. f(x) = 1 А— 1 - cos x 17. g(x) = c. What is the area k(h) of the green-shaded triangle? 1 – sin x 3 18. y = sin(2t³ + 1) d. Use the fact that g(h) < f (h) < k(h) for small h > 0 to prove that 19. y = In(sin x + cos x) 20. y = In(sec x + tan x) sin x lim 1 x→0 Use the given trigonometric identity in parentheses and the basic rules of differentiation to find the derivatives of the functions given in Problems 21 to 24. by beginning with the inequality BLUE AREA < PINK AREA < GREEN AREA 30. Prove.
Transcribed Image Text:PROBLEM SET 3.4 Level 1 DRILL PROBLEMS Level 2 APPLIED AND THEORY PROBLEMS Differentiate the functions given in Problems 1 to 20. 29. Consider three areas as shown in Figure 3.22. 1. f(x) = sin x + cos x 2. g(x) = 2 sin x + tan x 1 3. y = sin 2x sin h h 4. y = cos 2x cos h IT 5. f(t) = t2 + cos t + cos 4 JT 6. g(t) = 2 sec t +3 tant – tan 3 - 7. y = e-* sin x 8. y = tan x2 tan h 9. f(0) = sin? e 10. g(0) = cos² 0 11. y = cos x'01 = (cos x)101 13. p(t) = (t² + 2) sin t 1 = COS 12. y Figure 3.22 Triangles and a unit circle with subtended angle h. a. What is the area g(h) of the blue-shaded triangle? 14. у — х sec x b. What is the area f(h) of the pink-shaded sector? sin t 15. q(t) Hint: The area of a sector of a circle of radius r and central angle 0 measured in radians is sin x 16. f(x) = 1 А— 1 - cos x 17. g(x) = c. What is the area k(h) of the green-shaded triangle? 1 – sin x 3 18. y = sin(2t³ + 1) d. Use the fact that g(h) < f (h) < k(h) for small h > 0 to prove that 19. y = In(sin x + cos x) 20. y = In(sec x + tan x) sin x lim 1 x→0 Use the given trigonometric identity in parentheses and the basic rules of differentiation to find the derivatives of the functions given in Problems 21 to 24. by beginning with the inequality BLUE AREA < PINK AREA < GREEN AREA 30. Prove.
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