# How to find the limit of the function mentioned below?

#### OmarMohamedKhallaf

##### New member
$$\displaystyle \lim\limits_{x \to 1}\frac{x^{\frac{13}{2}}-x^{\frac{1}{2}}}{x^{\frac{7}{2}}-x^{\frac{1}{2}}}$$
What I did:
$$\displaystyle \lim\limits_{x \to 1}\frac{x^{\frac{13}{2}}-x^{\frac{1}{2}}}{x^{\frac{7}{2}}-x^{\frac{1}{2}}}=\lim\limits_{x \to 1}\frac{x^{\frac{1}{2}}(x^{13}-1)}{x^{\frac{1}{2}}(x^{7}-1)}=\lim\limits_{x \to 1}\frac{x^{13}-1^{13}}{x^{7}-1^{7}}=\frac{13}{7}\times 1^{13-7}=\frac{13}{7}$$
But the answer seems to be 2. Where did I go wrong?

#### topsquark

##### Full Member
$$\displaystyle \lim\limits_{x \to 1}\frac{x^{\frac{13}{2}}-x^{\frac{1}{2}}}{x^{\frac{7}{2}}-x^{\frac{1}{2}}}$$
Take a closer look at when you factored $$\displaystyle x^{13/2}$$
$$\displaystyle x^{13/2} = x^{1/2} \cdot x^{13/2 - 1/2} = x^{1/2} \cdot x^{12/2} = x^{1/2} \cdot x^6$$

-Dan