Question

$f ( x )$ is continuous at $x =0$, then which of the following are always true?

• A. $\underset {x \rightarrow 0} {\text{Lim}}f(x)=0$
• B. $f(x)$ is non continuous at $x=1$
• C. $g ( x )= x ^2 f ( x )$ is continuous at $x =0$
• D. $\underset{x \rightarrow 0^{+}}{\text{Lim}} (f(x)-f(0))=0$

Answer 1

Answer: (C), (D)

Correct answer is (c) $g ( x )= x ^2 f ( x )$ is continuous at $x =0$Correct answer is (d) $\underset{x \rightarrow 0^{+}}{\text{Lim}} (f(x)-f(0))=0$