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48. Let f(x)=1/x and g(x)=1/x^2. (a) Find (f∘g)(x). (b) Is f∘g continuous everywhere? Explain.

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47. Suppose f and g are continuous functions such that g(2)=6 and (lim)(x→2)[3f(x)+f(x)g(x)]=36.

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

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45. For what value of the constant c is the function f continuous on (-∞,∞)? f(x)={cx^2+2x if x⋖2,

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The Limit Definition You Never Understood: The Precise Definition of a Limit

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43. Find the numbers at which f is discontinuous. At which of these numbers is f continuous from the

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42. Find the numbers at which f is discontinuous. At which of these numbers is f continuous from the

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41. Find the numbers at which f is discontinuous. At which of these numbers is f continuous from the

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40. Show that f is continuous on (-∞,∞). f(x)={sin⁡x if x⋖π/4, cos⁡x if x≥π/4

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37. Use continuity to evaluate the limit. lim⁡(x→1) ln⁡((5-x^2)/(1+x))

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36. Use continuity to evaluate the limit. lim⁡(x→π)sin⁡(x+sin⁡x)

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35. Use continuity to evaluate the limit. lim⁡(x→2)x√(20-x)

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34. Locate the discontinuities of the function and illustrate by graphing. y=ln⁡((tan^2⁡x))

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33. Locate the discontinuities of the function and illustrate by graphing. y=1/(1+e^(1/x))

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

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

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

0:02:49

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

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

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24. How would you “remove the discontinuity” of f? In other words, how would you define f(2) in ord

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23. How would you “remove the discontinuity” of f? In other words, how would you define f(2) in ord

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

0:02:44

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

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