Find the limit of ((1+x)^(1/2))/(4+4x) as x approaches -1

 Exercise

$\lim_{x\to-1}\left(\frac{\sqrt{1+x}}{4+4x}\right)$

 

Factor the polynomial $4+4x$ by it's greatest common factor (GCF): $4$

$\lim_{x\to-1}\left(\frac{\sqrt{1+x}}{4\left(1+x\right)}\right)$

 

Simplify the fraction $\frac{\sqrt{1+x}}{4\left(1+x\right)}$ by $1+x$

$\lim_{x\to-1}\left(\frac{\left(1+x\right)^{-\frac{1}{2}}}{4}\right)$

 

Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number

$\lim_{x\to-1}\left(\frac{1}{4\sqrt{1+x}}\right)$

 

Evaluate the limit $\lim_{x\to-1}\left(\frac{1}{4\sqrt{1+x}}\right)$ by replacing all occurrences of $x$ by $-1$

The limit does not exist

The limit does not exist

 Try other ways to solve this exercise

Can't find a method? Tell us so we can add it.