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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
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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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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