If f(x) = x sin1/x , x ≠ 0 then the value of the function at x = 0, so that the function is continuous at x = 0, is A. 0 B. –1

Question

If f(x) = x sin \(\frac{1}{x}\), x ≠ 0 then the value of the function at x = 0, so that the function is continuous at x = 0, is 

A. 0 

B. –1 

C. 1 

D. none of these

Answer 1

Option : (A)

Formula :-

(i) A function f(x) is said to be continuous at a point x = a of its domain, if
\(\lim\limits_{x \to a}f(x)\) = f(a)
\(\lim\limits_{x \to a^+}f(a+h)\) = \(\lim\limits_{x \to a^-}f(a-h)\) = f(a) 

(ii) Standard limits 

\(\lim\limits_{x \to 0}\frac{sinx}{x}\) = 1

Given :-