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. Evaluate lim √²-9. X-5

. Evaluate lim √²-9. X-5

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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9, 11, 17, 19, 21, 27, 41, 45, 47 these are the one's I need help with

Assign ← → C 845247 Assign 44°F Mostly cloudy Learnin A-Z Da JSTOR E Science PQ Repres E Result learn-us-east-1-prod-fleet02-xythos.content.blackboardcdn.com/5fda9d7e7f5d0/845247?X-Blackboard-S3-Bucket-learn-us-east-1-prod-fleet01-xythos&X-Bl... SECTION 2.3 EXERCISES Review Questions 1. How is lim f(x) calculated if f is a polynomial function? xa 2. How are lim f(x) and lim f(x) calculated if f is a polynomial function? 4. 3. For what values of a does lim r(x) = r(a) if r is a rational function? 5. Explain why lim 6. Assume lim g(x) = 4 and f(x) = g(x) whenever x 3. Evalu- x-3 ate lim f(x), if possible. ² - 7x + 12 x 3 If flim f(x) = -8, find lim (f(x))²/3 x-2 H 99 / 1442 p(x) 7. Suppose p and q are polynomials. If lim = 10 and 0 g(x) q(0) = 2, find p(0). ▬▬ 8. Suppose lim f(x) = lim h(x) = 5. Find lim g(x), where f(x) = g(x) ≤ h(x), for all x x 9. Evaluate lim V-9. 10. Suppose x-5 f(x) = = lim (x-4). x-3 S4 QUICK CHECK 4 Suppose f satisfies 1 ≤ f(x) = 1 + lim f(x), if possible. < x-0 Compute lim f(x) and lim f(x). x-3 x + 2 O Search Connec Bb class fil Bb 841212 Bb 845 X Bb 845247 b Succes: + if x ≤ 3 ifx > 3. 100% + A » Basic Skills 11-16. Limits of linear functions Evaluate the following limits. 11. lim (3x - 7) 12. lim (-2x + 5) 15. lim 4 x-6 14. lim (-3x) X-22 17. lim (4f(x)) x-1 19. lim (f(x) g(x)) x-1 Pl 17-24. Applying limit laws Assume lim f(x) = 8, lim g(x) = 3, and lim h(x) = 2. Compute the following limits and state the limit laws used to justify your computations. 21. lim 23. lim (h(x))5 x-1 27. lim M f for all values of x near zero. Find f(x)g(x) h(x) 25-32. Evaluating limits Evaluate 25. lim (2x³ 3x² + 4x + 5) 5x² + 6x +1 8x4 3b b2 V4b + 1-1 29. lim a 13. lim 5x →-9 18. lim 16. lim # X-5 f(x) x→1 h(x) 20. lim (f(x)h(x)) 22. lim f(x) x-1 g(x) - h(x) 24. lim Vf(x)g(x) + 3 the following limits. 26. lim (²2+5 + 7) 1-2 28. lim V² 10 13 30. lim (x²-x)5 x-2 ☆ R 4x O ☐ 11:34 PM 2/7/2023 ⠀ X
Transcribed Image Text:Assign ← → C 845247 Assign 44°F Mostly cloudy Learnin A-Z Da JSTOR E Science PQ Repres E Result learn-us-east-1-prod-fleet02-xythos.content.blackboardcdn.com/5fda9d7e7f5d0/845247?X-Blackboard-S3-Bucket-learn-us-east-1-prod-fleet01-xythos&X-Bl... SECTION 2.3 EXERCISES Review Questions 1. How is lim f(x) calculated if f is a polynomial function? xa 2. How are lim f(x) and lim f(x) calculated if f is a polynomial function? 4. 3. For what values of a does lim r(x) = r(a) if r is a rational function? 5. Explain why lim 6. Assume lim g(x) = 4 and f(x) = g(x) whenever x 3. Evalu- x-3 ate lim f(x), if possible. ² - 7x + 12 x 3 If flim f(x) = -8, find lim (f(x))²/3 x-2 H 99 / 1442 p(x) 7. Suppose p and q are polynomials. If lim = 10 and 0 g(x) q(0) = 2, find p(0). ▬▬ 8. Suppose lim f(x) = lim h(x) = 5. Find lim g(x), where f(x) = g(x) ≤ h(x), for all x x 9. Evaluate lim V-9. 10. Suppose x-5 f(x) = = lim (x-4). x-3 S4 QUICK CHECK 4 Suppose f satisfies 1 ≤ f(x) = 1 + lim f(x), if possible. < x-0 Compute lim f(x) and lim f(x). x-3 x + 2 O Search Connec Bb class fil Bb 841212 Bb 845 X Bb 845247 b Succes: + if x ≤ 3 ifx > 3. 100% + A » Basic Skills 11-16. Limits of linear functions Evaluate the following limits. 11. lim (3x - 7) 12. lim (-2x + 5) 15. lim 4 x-6 14. lim (-3x) X-22 17. lim (4f(x)) x-1 19. lim (f(x) g(x)) x-1 Pl 17-24. Applying limit laws Assume lim f(x) = 8, lim g(x) = 3, and lim h(x) = 2. Compute the following limits and state the limit laws used to justify your computations. 21. lim 23. lim (h(x))5 x-1 27. lim M f for all values of x near zero. Find f(x)g(x) h(x) 25-32. Evaluating limits Evaluate 25. lim (2x³ 3x² + 4x + 5) 5x² + 6x +1 8x4 3b b2 V4b + 1-1 29. lim a 13. lim 5x →-9 18. lim 16. lim # X-5 f(x) x→1 h(x) 20. lim (f(x)h(x)) 22. lim f(x) x-1 g(x) - h(x) 24. lim Vf(x)g(x) + 3 the following limits. 26. lim (²2+5 + 7) 1-2 28. lim V² 10 13 30. lim (x²-x)5 x-2 ☆ R 4x O ☐ 11:34 PM 2/7/2023 ⠀ X
Assign ← → C 845247 Assign 44°F Mostly cloudy Learnin A-Z Da JSTOR E Science PQ Repres b. Explain why lim learn-us-east-1-prod-fleet02-xythos.content.blackboardcdn.com/5fda9d7e7f5d0/845247?X-Blackboard-S3-Bucket-learn-us-east-1-prod-fleet01-xythos&X-Bl... 39. lim x-3√2-x 37. Absolute value limit Show that lim |x| = 0 by first evaluating lim |x and lim x. Recall that x-0 x-0 10¹ 41. lim 43. lim x-b 38. Absolute value limit Show that lim |x| = |a|, for any real number. (Hint: Consider the cases a < 0 and a ≥ 0.) 45. lim 47. lim 39-52. Other techniques Evaluate the following limits, where a and b are fixed real numbers. 1²-1 xx-1 1². - 16 x-44-x √x - 3 x9x-9 (x - b) 50 - x + b x-b (2x - 1)²-9 x+1 49. lim. 48. lim 4t x-a - Jx |x| = xaVx Va H ▬▬ - does not exist. 100 / 1442 a>0 O Search if x 20 -x if x < 0. E Result 1 2² 23 ) (6 + 1 - 1²)) 40. lim 42. limi 44. lim 46. lim x²2x3 x 3 31²-71 +2 2-1 (x + b)² + (x + b) ¹⁰ 4(x + b) Connec Bb class fil Bb 841212 Bb 845 X Bb 845247 b Succes: + 5+4-3 h x²-a² √x - √> 0 50. lim- 100% + A » a x 3 - 1 x T56. -0.1 -0.01 -0.001 -0.0001 0.0001 0.001 0.01 0.1 T55. Applying the Squeeze Theorem 1 a. Show that -|x ≤ x sin = ≤ |x|, for x = 0. x b. Illustrate the inequalities in part (a) with a graph. 1 c. Use the Squeeze Theorem to show that lim x sin = 0. 10) A cosine limit by the Squeeze Theorem It can be shown that 1- cos x ≤ 1, for x near 0. a. Illustrate these inequalities with a graph. b. Use these inequalities to evaluate lim cos x x0 T57. A sine limit by the Squeeze Theorem It can be shown that x² sin.x 1 6 x a. Illustrate these inequalities with a graph. sin x b. Use these inequalities to evaluate lim x0 x S ≤ 1, for x near 0. T58. A logarithm limit by the Squeeze Theorem a. Draw a graph to verify that-x ≤ x² Inx²s x, for -1 ≤ x ≤ 1, where x 0. b. Use the Squeeze Theorem to evaluate lim x² In.x². x-0 ☆ R 4x O ☐ 11:34 PM 2/7/2023 ⠀ X
Transcribed Image Text:Assign ← → C 845247 Assign 44°F Mostly cloudy Learnin A-Z Da JSTOR E Science PQ Repres b. Explain why lim learn-us-east-1-prod-fleet02-xythos.content.blackboardcdn.com/5fda9d7e7f5d0/845247?X-Blackboard-S3-Bucket-learn-us-east-1-prod-fleet01-xythos&X-Bl... 39. lim x-3√2-x 37. Absolute value limit Show that lim |x| = 0 by first evaluating lim |x and lim x. Recall that x-0 x-0 10¹ 41. lim 43. lim x-b 38. Absolute value limit Show that lim |x| = |a|, for any real number. (Hint: Consider the cases a < 0 and a ≥ 0.) 45. lim 47. lim 39-52. Other techniques Evaluate the following limits, where a and b are fixed real numbers. 1²-1 xx-1 1². - 16 x-44-x √x - 3 x9x-9 (x - b) 50 - x + b x-b (2x - 1)²-9 x+1 49. lim. 48. lim 4t x-a - Jx |x| = xaVx Va H ▬▬ - does not exist. 100 / 1442 a>0 O Search if x 20 -x if x < 0. E Result 1 2² 23 ) (6 + 1 - 1²)) 40. lim 42. limi 44. lim 46. lim x²2x3 x 3 31²-71 +2 2-1 (x + b)² + (x + b) ¹⁰ 4(x + b) Connec Bb class fil Bb 841212 Bb 845 X Bb 845247 b Succes: + 5+4-3 h x²-a² √x - √> 0 50. lim- 100% + A » a x 3 - 1 x T56. -0.1 -0.01 -0.001 -0.0001 0.0001 0.001 0.01 0.1 T55. Applying the Squeeze Theorem 1 a. Show that -|x ≤ x sin = ≤ |x|, for x = 0. x b. Illustrate the inequalities in part (a) with a graph. 1 c. Use the Squeeze Theorem to show that lim x sin = 0. 10) A cosine limit by the Squeeze Theorem It can be shown that 1- cos x ≤ 1, for x near 0. a. Illustrate these inequalities with a graph. b. Use these inequalities to evaluate lim cos x x0 T57. A sine limit by the Squeeze Theorem It can be shown that x² sin.x 1 6 x a. Illustrate these inequalities with a graph. sin x b. Use these inequalities to evaluate lim x0 x S ≤ 1, for x near 0. T58. A logarithm limit by the Squeeze Theorem a. Draw a graph to verify that-x ≤ x² Inx²s x, for -1 ≤ x ≤ 1, where x 0. b. Use the Squeeze Theorem to evaluate lim x² In.x². x-0 ☆ R 4x O ☐ 11:34 PM 2/7/2023 ⠀ X
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