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19. Explain why the function is discontinuous at the given number. Sketch the graph of the function.

18. Explain why the function is discontinuous at the given number. Sketch the graph of the function.

17. Explain why the function is discontinuous at the given number. Sketch the graph of the function.

16. Use the definition of continuity and the properties of limits to show that the function is

15. Use the definition of continuity and the properties of limits to show that the function is

14. Use the definition of continuity and the properties of limits to show that the function is

13. Use the definition of continuity and the properties of limits to show that the function is

11. Use the definition of continuity and the properties of limits to show that the function is

10. Explain why each function is continuous or discontinuous.

9. The toll T charged for driving on a certain stretch of a toll road is $5 except during rush hours

8. Sketch the graph of f that is continuous except for the stated discontinuity . Neither left nor

7. Sketch the graph of f that is continuous except for the stated discontinuity. Removable

6. Sketch the graph of f that is continuous except for the stated discontinuity. Discontinuities

5. Sketch the graph of f that is continuous except for the stated discontinuity. Discontinuous,

4. From the graph of g, state the intervals on which g is continuous.

3. From the graph of f, state the numbers at which f is discontinuous and explain why.

2. If f is continuous on (-∞,∞), what can you say about its graph?

1. Write an equation that expresses the fact that a function f is continuous at the number 4.

40. By comparing Definitions 2, 3, and 4, prove Theorem 2.3.1.

37. Prove that lim⁡(x→a) √x=√a if a≻0. [Hint: Use |√x-√a|=|x-a|/(√x-√a).]

36. Prove that lim⁡(x→2)1/x=1/2.

33. Verify that another possible choice of δ for showing that (lim⁡)(x→3) x^2=9 in Example 4 is

Glencoe Algebra 1: Chapter 0 Part 1

28. Prove the statement using the ε, δ definition of a limit. (lim⁡)(x→-6^)8√(6+x)=0