Question

Evaluate:$\underset{x\to 0}{lim}\left({\left(x+1\right)}^{\frac{2}{3}}-{\left(x-1\right)}^{\frac{2}{3}}\right)$

Answer 1

$\underset{x\to 0}{lim}\left(\right(x+1{)}^{\frac{2}{3}}-(x-1{)}^{\frac{2}{3}})$

this is not at form $\frac{0}{0}$

So just put the values

$(1{)}^{\frac{2}{3}}-(-1{)}^{\frac{2}{3}}$

cube root of $-1$ is $-1$

then square of $1$ is $1$

$=1-1$

$=0$