Evaluate lim x->1

Question

Help please ASAP

Answer 1

Let x=1+h, then the fraction becomes ((1+h)^⅓-1)/((1+h)^¼-1). Call this ①.

We can expand (1+h)^⅓=1+h/3+... and (1+h)^¼=1+h/4+... to the first approximations when h is small.

Substitute these: h/3÷(h/4)=4/3 because the leading 1 cancels with the -1 in ①.

When x➝1, h➝0, so the limit is 4/3.