If `f(x)={(1-cos10x)/(x^2a),x<0(sqrt(x))/(sqrt(625)+sqrt(x)-25),x >0,x=0` then the value of a so that `f(x)` may be continuous at `x=0,i s` 25 (b) `-1` (c) 1 (d) indeterminate

Explanation

`lim_(x->0) (1-cos10x)/x^2`

`lim_(x->0) (10(sin 10x))/(2x)`

`lim_(x->0) (5sin10x)/x xx 10/10 = 50`

`a=50`

now,`lim_(x->0) (sqrtx)/(sqrt(625 + sqrtx) - 25)`

`lim_(x->0) 2sqrt(625 + sqrtx)`

`=50`

option b is correct