Assertion (A): f(x) = | x | is continuous at x = 0. Reason (R): f(x) = | x | is differentiable at x = 0.

Continuity & Differentiability · Question 92 of 125

Question 92

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Assertion (A): $f(x) = \lvert x \rvert$ is continuous at $x = 0$ .
Reason (R): $f(x) = \lvert x \rvert$ is differentiable at $x = 0$ .

Both A and R are true, and R is the correct explanation of A.Correct answerYour answerBoth A and R are true, but R is not the correct explanation of A.Correct answerYour answerA is true, but R is false.Correct answerYour answerA is false, but R is true.Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

A is true: both one-sided limits are 0, equal to $f(0)$ .
R is false: the one-sided derivatives are $-1$ and 1.

Concept: A corner: continuous, not differentiable
Typical timeTypical: 90 s
Your timeYours: —

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Assertion (A): f(x)=∣x∣f(x) = \lvert x \rvertf(x)=∣x∣ is continuous at x=0x = 0x=0.Reason (R): f(x)=∣x∣f(x) = \lvert x \rvertf(x)=∣x∣ is differentiable at x=0x = 0x=0.

Explanation

Assertion (A): $f(x) = \lvert x \rvert$ is continuous at $x = 0$ .
Reason (R): $f(x) = \lvert x \rvert$ is differentiable at $x = 0$ .