The value of `f(0)` so that the function `f(x)=(2-(256-7x)^(1/8))/((5x+32)^(1//5)-2),x!=0` is continuous everywhere, is given by `-1` (b) 1 (c) 26 (d) none of these

Explanation

Correct option is A)

`f(x)=(2-(256-7x)^(1/8))/((5x+32)^(1//5)-2)`

For f(x) to be continuous everywhere

`lim​_(x→0)f(x)=`finite

`⇒lim​_(x→0)​`f(x)=(2-(256-7x)^(1/8))/((5x+32)^(1//5)-2)` 0/0 ` form


`=>lim​_(x→0)(0−1/8​(256−7x)^(−7/8)×(−7)​)/(1/5​(5x+32)^(−4/5)(5)−0)`

`=(7×2^4)/(8×2^7)​`

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