Concept explainers
a.
If f is continuous at x =0,find the value of b. Justify your answer.
a.
Answer to Problem 53RE
Explanation of Solution
Given information: Let
Calculation:
Set the two equations equal to each other since being continuous means their limits are equal.
If the right side equation equals 3 then, in order to be continuous, the left side equation must equal 3 as well.
b.
If f is differentiable atx =0,find the value of a. Justify your answer.
b.
Answer to Problem 53RE
Explanation of Solution
Given information: Let
Calculation:
For f(x) to be differentiable at x =0 ,it must be continuous at x =0 so substitute b =3 that we found from part (a ).
c.
Is f is differentiable at x =0,if a =5 and b =4. Justify your answer.
c.
Answer to Problem 53RE
No,
Explanation of Solution
Given information: Let
Calculation:
No, From part (a), f(x) is only continuous at x =0 if b =3 .For a function to be differentiable ,it must be continuous so if b =4 , f(x) is discontinuous at x =0 and therefore not differentiable at x =0.
Chapter 4 Solutions
Calculus: Graphical, Numerical, Algebraic
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