If the function f(x) defined by f(x) = {[(log(1+3x)-log(1-2x))/x,x≠0][k,x=0] is continuous at x = 0, then k = A. 1 B. 5 C. -1 D. None of these. ​

Question

If the function f(x) defined by\(f(x) = \begin{cases}\frac{log(1+3x)-log(1-2x)}{x} &,x≠0\\ k &, x=0\\\end{cases} \) , is continuous at x = 0, then k =

A. 1

B. 5

C. -1

D. None of these.

Answer 1

Option : (B)

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) 

= 5 (Using standard limit)

Function f(x) is continuous at x = 0

⇒ 5 = k