The function f(x) = (ln (1+ax)- ln(1 - bx) /x) is not defined at x = 0. The value which should be assigned to f at x = 0 so that it is continuous at x = 0, is

Question

The function f(x) = (ln (1+ax)- ln(1 - bx) /x) is not defined at x = 0. The value which should be assigned to f at x = 0 so that it is continuous at x = 0, is (A) a - b (B) a + b (C) ln a - ln b (D) none of these

Tardigrade Admin · Accepted Answer

For f (x) to be continuous at x = 0 f(0) = displaystyle limx → 0 f(x) = displaystyle limx → 0 (ln(1+ax) - ln(1-bx)/x) [ textUsing limx →0 ( ln(1+x)/x) = 1] = a+b

Q. The function $f (x) = \frac{l n ( 1 + a x ) - l n ( 1 - b x )}{x}$ is not defined at x = 0. The value which should be assigned to f at x = 0 so that it is continuous at x = 0, is

$a - b$

$a + b$

ln a - ln b

none of these

For $f (x)$ to be continuous at $x = 0$
$f (0) = x \to 0 lim f (x)$
$= x \to 0 lim \frac{l n ( 1 + a x ) - l n ( 1 - b x )}{x}$
$[Using lim_{x \to 0} \frac{l n ( 1 + x )}{x} = 1]$
$= a + b$

Q. The function f(x)=xln(1+ax)−ln(1−bx)​ is not defined at x = 0. The value which should be assigned to f at x = 0 so that it is continuous at x = 0, is

a−b

a+b