zpupster 3 years ago lim x-->1 x^1/3 -1 over x^1/4 - 1

1. anonymous

$\lim_{x \rightarrow 1}\frac{x^\frac{1}{3}-1}{x^\frac{1}{4}-1}$ use L'hospital' rule to simplify the statement, as the limit results to 0/0

2. hartnn

just an alternate way, you could divide numerator and denominator by x-1 and use the standard limit, $$\Large \lim \limits_{x\rightarrow a} \dfrac{x^n-a^n}{x-a}=na^{n-1}$$

3. anonymous

$\frac{ x^m-a }{ x^n-a}=\frac{ m }{ n }.a ^{m-n}$

4. anonymous

you can also try $x=y^{12}\\x^{1/3}=y^4,\quad x^{1/4}=y^3$ also, when $x\rightarrow 1,\quad y\rightarrow 1$