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

Question

f ( x ) is continuous at x =0, then which of the following are always true? (A)  underset x arrow 0 textLimf(x)=0 (B) f(x) is non continuous at x=1 (C) g ( x )= x 2 f ( x ) is continuous at x =0 (D)  undersetx arrow 0+ textLim (f(x)-f(0))=0

Tardigrade Admin · Accepted Answer

Correct answer is (c) g ( x )= x 2 f ( x ) is continuous at x =0Correct answer is (d) undersetx arrow 0+ textLim (f(x)-f(0))=0

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

$x \to 0 Lim f (x) = 0$

$f (x)$ is non continuous at $x = 1$

$g (x) = x^{2} f (x)$ is continuous at $x = 0$

$x \to 0^{+} Lim (f (x) - f (0)) = 0$

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

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

x→0Lim​f(x)=0

f(x) is non continuous at x=1

g(x)=x2f(x) is continuous at x=0

x→0+Lim​(f(x)−f(0))=0