Question

if function f(x) = √1+x -√1+x⅓ is continuous function at x=0, then f(0) is equal to. The answer is 1/6 i need step by step solution

Answer 1

at x = 0 function is continuous , this is possible only when ,
Lim(x→0) f(x) = finite and exist

now,
Lim(x→0) { √(1 + x) - ³√(1 + x)}/x
Lim(x→0) [{ (1 + x)½ - 1½} -{(1 + x)⅓ - 1⅓ }]/x
Lim(x→0) [1/2x - 1/3x ] /x
Lim(x→0) x/6x = 1/6