Questions from Calculus


Q: Use the Intermediate Value Theorem and a graphing utility to approximate the

Use the Intermediate Value Theorem and a graphing utility to approximate the zero of the function in the interval [0, 1]. Repeatedly “zoom in” on the graph of the function to approximate the zero accu...

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Q: Verify that the Intermediate Value Theorem applies to the indicated interval and

Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c guaranteed by the theorem. f(x) = x2 + x − 1, [0, 5], f(c) = 11

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Q: Verify that the Intermediate Value Theorem applies to the indicated interval and

Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c guaranteed by the theorem. f(x) = x2 - 6x + 8, [0, 3], f(c) = 0

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Q: Verify that the Intermediate Value Theorem applies to the indicated interval and

Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c guaranteed by the theorem. f(x) = √x + 7 – 2, [0, 5], f(c) = 1

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Q: Verify that the Intermediate Value Theorem applies to the indicated interval and

Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c guaranteed by the theorem. f(x) = ∛x + 8, [-9, -6], f(c) = 6

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Q: Sketch the graph of f′. Explain how you found your answer

Sketch the graph of f′. Explain how you found your answer.

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Q: Verify that the Intermediate Value Theorem applies to the indicated interval and

Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c guaranteed by the theorem. f(x) = x – x3 / x - 4, [1, 3], f(c) = 3

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Q: Write a function that is continuous on (a, b)

Write a function that is continuous on (a, b) but not continuous on [a, b].

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Q: Sketch the graph of any function f such that /

Sketch the graph of any function f such that Is the function continuous at x = 3? Explain.

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Q: If the functions f and g are continuous for all real x

If the functions f and g are continuous for all real x, is f + g always continuous for all real x? Is f / g always continuous for all real x? If either is not continuous, give an example to verify you...

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