- #1
efekwulsemmay
- 54
- 0
Homework Statement
All the problem is asking me to do is find the limit. I have to do it algebraicly too which sucks. I can't figure out how to do it.
[tex]\lim_{x\rightarrow0} \frac{\frac{1}{x+2}-\frac{1}{2}}{x}[/tex]
Homework Equations
I am not sure really.
The Attempt at a Solution
One thing I have tried is to multiply by [tex]\frac {x}{x}[/tex]. Which gave me:
[tex]\lim_{x\rightarrow0} \frac{\frac{1}{x+2}-\frac{1}{2}}{x} \times \frac {x}{x}[/tex]
[tex]=\frac{\frac{1\times x}{x+2}-\frac{1\times x}{2}}{x\times x}[/tex]
[tex]= \frac{\frac{x}{x+2}-\frac{x}{2}}{x^{2}}[/tex]
[tex]=\frac{x}{x+2}\rightarrow \frac{x}{x}+\frac{x}{2} \rightarrow 1+\frac{x}{2}[/tex]
[tex]=\frac{1+\frac{x}{2}-\frac{x}{2}}{x^{2}}[/tex]
[tex]=\frac{1}{x^{2}}[/tex]
1) I am not sure of my algebra during this and
2) I don't know where to go from here should my algebra check out.
I have already tried to multiply by [tex]\frac{\sqrt{x}}{\sqrt{x}}[/tex] but it just seems to give me [tex]\frac{\sqrt{x}}{x}[/tex] which doesn't help. I am stuck help me please?