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2 + 7x if x < 4 Let f(x) if x 2 4. For what value of the constant c is the function f continuous on (-o, c0)?

2 + 7x if x < 4 Let f(x) if x 2 4. For what value of the constant c is the function f continuous on (-o, c0)?

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter8: Functions
Section8.2: Linear Functions And Applications
Problem 33PS
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2 + 7x if x < 4 Let f(x) if x 2 4. For what value of the constant c is the function f continuous on (-o, c0)?
Transcribed Image Text:2 + 7x if x < 4 Let f(x) if x 2 4. For what value of the constant c is the function f continuous on (-o, c0)?
Expert Solution
Step 1

Given function is:

fx=cx2+7x       if x<4x3-cx          if x≥4

We know that a function is continuous at x=a if

limx→afx=fa

Here, we can to check the continuity at x=4, as it is continuous at  everywhere else.

As function to be continuous in -∞,∞ it should also be continuous at x=4.

Therefore,

limx→4-fx=limx→4+fx

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