Homework Help is Here – Start Your Trial Now!
Math
Calculus
et 1+e* OShow that f(x) > 1/2 for all x2 0. (a) JHINT: e' 21 for all x>0.] isc the inequality in part (a) to show that diverges. ()dr

et 1+e* OShow that f(x) > 1/2 for all x2 0. (a) JHINT: e' 21 for all x>0.] isc the inequality in part (a) to show that diverges. ()dr

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 78E
See similar textbooks
icon
Related questions
Topic Video
Question
#26 #4
VTUIOR O89OA2JA T In Exercises 11-14, find a value for the parameter a that makes 10.2 Delecting Convergence, Estimating Limits y lar 1+e" Show that f (x) > 1/2 for all x > 0. IHINT: e' > 1 for all x > 0.] Ise the inequality in part (a) to show that the value of the improper integral less than 10 $37 we'll 1. vark e dx 12. e da diverges. 13. dx 5 Let f(x) =r + sin.x. Show that x – 1< S(x) for all x > 0. 14. - In Exercises I5-18, find a proper integral whose value approt- ds imates that of the given (convergent) improper integral within x (In x) Usc the inequality in part (a) to show that dx 10-5 S(x) diverges. 15. dx 6 Let f(x)=x² + sin x. a Show that r – 1s S(x) for all x > 0 dx arctan x dx 17. dx (1+x) 18. O) Does T converge? Justify your answer. f(x) 19. Suppose that f(x)20 for all x21 and that 7. Let (x) = x² + /ĩ. (2) Show that x2 < [(x) for all x > 0. converges. Explain why there is a number a such that | S(x) dx < 10 ". dx (h) Use the inequality in part (a) to show that f(x) 20. Suppose that g(x) 20 for all x21 and that converges. diverges. Explain why there is a number b'such that Let (a)=r-. g(x)dx 2 10". 6) Show that x2/2 < f(x) for all x > 2. dx (b) Does , T) converge? Justify your answer. 1%3 S(x)dx comverges and that 21. Suppose that dx converge? Justify your answer. )d<0.0001.Show that|7 – " sc«) da|s0.0 S0.001. 9. Does メーVズ dx converge? Justify your answer. 22. Show that 0.8 < sin (e") dx < 1. 10. Does [HINT: Use the substitution u = e.] or FURTHER EXERCISES tal dx dx L e“ dx converges. [HINT: See Example 5 29. VI(1+x) 23. Show that but be careful: e- >e- for some x 2 0. dx e dx converge? Justify your answer. 31. Does 24. Consider the integral I = (In x) " cos X dx diverges. in (a) Show that In xs VI for all x> 2. 32. Show that the integral (b) Does I converge? Justify your answer. cosx dx dx converges. 31, TInx) 33. (a) Show that K. Suppose that p>1 is a constant and that / = (b) Use integration by parts and part (a) to show that For which values of p, if any, does I converge? Justify your (In x)" = 0.] sin.x dx converges. answer. [HINT: lim dx Show that 0</ <3. 34. Let I = | ja) Show that 0 <x/2< sin.x if 0 <x<l. [HINT: 1/2 < cos.x if 0 <x < 1.] (b) Use the inequality in part (a) to show that 26. dx Vitedi Vsin x 35. Evaluate lim converges. 36. Evaluate lim e le" dt. mproper integral converges or diverges. dx 27. dx 28.
Transcribed Image Text:VTUIOR O89OA2JA T In Exercises 11-14, find a value for the parameter a that makes 10.2 Delecting Convergence, Estimating Limits y lar 1+e" Show that f (x) > 1/2 for all x > 0. IHINT: e' > 1 for all x > 0.] Ise the inequality in part (a) to show that the value of the improper integral less than 10 $37 we'll 1. vark e dx 12. e da diverges. 13. dx 5 Let f(x) =r + sin.x. Show that x – 1< S(x) for all x > 0. 14. - In Exercises I5-18, find a proper integral whose value approt- ds imates that of the given (convergent) improper integral within x (In x) Usc the inequality in part (a) to show that dx 10-5 S(x) diverges. 15. dx 6 Let f(x)=x² + sin x. a Show that r – 1s S(x) for all x > 0 dx arctan x dx 17. dx (1+x) 18. O) Does T converge? Justify your answer. f(x) 19. Suppose that f(x)20 for all x21 and that 7. Let (x) = x² + /ĩ. (2) Show that x2 < [(x) for all x > 0. converges. Explain why there is a number a such that | S(x) dx < 10 ". dx (h) Use the inequality in part (a) to show that f(x) 20. Suppose that g(x) 20 for all x21 and that converges. diverges. Explain why there is a number b'such that Let (a)=r-. g(x)dx 2 10". 6) Show that x2/2 < f(x) for all x > 2. dx (b) Does , T) converge? Justify your answer. 1%3 S(x)dx comverges and that 21. Suppose that dx converge? Justify your answer. )d<0.0001.Show that|7 – " sc«) da|s0.0 S0.001. 9. Does メーVズ dx converge? Justify your answer. 22. Show that 0.8 < sin (e") dx < 1. 10. Does [HINT: Use the substitution u = e.] or FURTHER EXERCISES tal dx dx L e“ dx converges. [HINT: See Example 5 29. VI(1+x) 23. Show that but be careful: e- >e- for some x 2 0. dx e dx converge? Justify your answer. 31. Does 24. Consider the integral I = (In x) " cos X dx diverges. in (a) Show that In xs VI for all x> 2. 32. Show that the integral (b) Does I converge? Justify your answer. cosx dx dx converges. 31, TInx) 33. (a) Show that K. Suppose that p>1 is a constant and that / = (b) Use integration by parts and part (a) to show that For which values of p, if any, does I converge? Justify your (In x)" = 0.] sin.x dx converges. answer. [HINT: lim dx Show that 0</ <3. 34. Let I = | ja) Show that 0 <x/2< sin.x if 0 <x<l. [HINT: 1/2 < cos.x if 0 <x < 1.] (b) Use the inequality in part (a) to show that 26. dx Vitedi Vsin x 35. Evaluate lim converges. 36. Evaluate lim e le" dt. mproper integral converges or diverges. dx 27. dx 28.
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer