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In this video we look at a function that has a discontinuity and we redefine it so that it is continuous at this discontinuity. I hope this ...

25. Explain, using Theorem's 4, 5, 7, 9, why the function is continuous at every number in its domain. State the domain.

32. Explain, using Theorem's 4, 5, 7, 9, why the function is continuous at every number in its domain. State the domain.

30. Explain, using Theorem's 4, 5, 7, 9, why the function is continuous at every number in its domain. State the domain.

27. Explain, using Theorem's 4, 5, 7, 9, why the function is continuous at every number in its domain. State the domain.

Full Playlist: https://www.youtube.com/playlist?list=PLJWhXkxQzDF5X5r_lpT20J1gEK152AcDu __________VIDEO ...

15. Use the definition of continuity and the properties of limits to show that the function is continuous on the given interval.

65. Prove that cosine is a continuous function. Calculus: Early Transcendentals Chapter 2: Limits and Derivatives Section 2.5: ...

39. Show that f is continuous on (-∞,∞). f(x)={(1-x^2 if x≤1, ln⁡x if x⋗1 Calculus: Early Transcendentals Chapter 2: Limits and ...

72. (a) Show that the absolute value function F(x)=|x| is continuous everywhere. (b) Prove that if f is a continuous function on an ...

71. Show that the function f(x)={x^4 sin⁡(1/x)if x≠0, 0 if x=0) is continuous on (-∞,∞). Calculus: Early Transcendentals Chapter 2: ...

26. Explain, using Theorem's 4, 5, 7, 9, why the function is continuous at every number in its domain. State the domain.

29. Explain, using Theorem's 4, 5, 7, 9, why the function is continuous at every number in its domain. State the domain.

31. Explain, using Theorem's 4, 5, 7, 9, why the function is continuous at every number in its domain. State the domain.

46. Find the values of a and b that make f continuous everywhere. F(x)={(x^2-4)/(x-2) if x⋖2, ax^2-bx+3 if 2≤x⋖3, 2x-a+b if x≥3 ...

64. To prove that sine is continuous, we need to show that lim(x→a)⁡sin⁡(a+h) =sin⁡a for every real number a. By Exercise 63 an ...

12. Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a.

10. Explain why each function is continuous or discontinuous. (a) The temperature at a specific location as a function of time.