If the function f(x) = (sin 10x)/x , x ≠ 0 is continuous at x = 0, find f(0). ​

Question

If the function f(x) = \(\frac{sin10x}{x}\), x ≠ 0 is continuous at x = 0, find f(0).

Answer 1

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

(ii) 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)

f(0) = 10