The value of f(0), so that the function f(x) = ((27-2x)^(1/3)-3)/(9-3(243+5x)^1/5 (x ≠ 0) is continuous, is given by : A = 2/5, B. 6, C.2, D.4 ​

Question

The value of f(0), so that the function f(x) = \(\frac{(27-2x)^{1/3}-3}{9-3(243+5x)^{1/5}}\)(x ≠ 0) is continuous, is given by :

A. \(\frac{2}{5}\) 

B. 6 

C. 2 

D. 4

Answer 1

Option : (C)

(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) \(\lim\limits_{x \to a}\{\frac{f(x)}{g(x)}\}\) = \(\frac{1}{m}\),

Where \(\lim\limits_{x \to a}f(x)\) = 1, \(\lim\limits_{x \to a}g(x)\) = m

Given :-