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(a) If f' is continuous, f(7) = 0, and f'(7) = 13, evaluate Limit: f(7+3x)+f(7+5x) lim x-0 Ꮖ (b) Now suppose that you don't know that f' is continuous, but rather you only were told that f'(7) = 13 and that f(7) = 0. Is your limiting value from (a) still true in this case? Hint: If you split the limit into two parts and subtract zero written in a clever way, you should see something that looks like a familiar definition. Note: This would make for a nice "apply your knowledge" test question. Moreover, on a test you would be expected to give an explanation.

(a) If f' is continuous, f(7) = 0, and f'(7) = 13, evaluate Limit: f(7+3x)+f(7+5x) lim x-0 Ꮖ (b) Now suppose that you don't know that f' is continuous, but rather you only were told that f'(7) = 13 and that f(7) = 0. Is your limiting value from (a) still true in this case? Hint: If you split the limit into two parts and subtract zero written in a clever way, you should see something that looks like a familiar definition. Note: This would make for a nice "apply your knowledge" test question. Moreover, on a test you would be expected to give an explanation.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.2: Polynomial Functions
Problem 96E: What is the purpose of the Intermediate Value Theorem?
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(a) If f' is continuous, f(7) = 0, and f'(7) = 13, evaluate Limit: f(7+3x)+f(7+5x) lim x-0 Ꮖ (b) Now suppose that you don't know that f' is continuous, but rather you only were told that f'(7) = 13 and that f(7) = 0. Is your limiting value from (a) still true in this case? Hint: If you split the limit into two parts and subtract zero written in a clever way, you should see something that looks like a familiar definition. Note: This would make for a nice "apply your knowledge" test question. Moreover, on a test you would be expected to give an explanation.
Transcribed Image Text:(a) If f' is continuous, f(7) = 0, and f'(7) = 13, evaluate Limit: f(7+3x)+f(7+5x) lim x-0 Ꮖ (b) Now suppose that you don't know that f' is continuous, but rather you only were told that f'(7) = 13 and that f(7) = 0. Is your limiting value from (a) still true in this case? Hint: If you split the limit into two parts and subtract zero written in a clever way, you should see something that looks like a familiar definition. Note: This would make for a nice "apply your knowledge" test question. Moreover, on a test you would be expected to give an explanation.
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