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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.

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 ...

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

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

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

Exam 1 Question 6 Part 2.

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

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

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

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

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

6. Sketch the graph of f that is continuous except for the stated discontinuity. Discontinuities at -1 and 4, but continuous from the ...

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

2. If f is continuous on (-∞,∞), what can you say about its graph? Calculus: Early Transcendentals Chapter 2: Limits and ...

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 ...

52. Suppose f is continuous on [1,5] and the only solutions of the equation f(x)=6 are x=1 and x=4. If f(2)=8, explain why f(3)⋗6.

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

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