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2.) limit as x---->infinity$\displaystyle \frac{x^2}{x^2-1}-\frac{x^3+1}{x^4+1}$

Do I find a common denominator first, subtract the fractions, and take it from there?

Note that if you multiply the first fraction by $\displaystyle \frac{\frac{1}{x^2}}{\frac{1}{x^2}}$, you get $\displaystyle \frac{1}{1-\frac{1}{x^2}}$; if you multiply the second fraction by $\displaystyle \frac{\frac{1}{x^4}}{\frac{1}{x^4}}$, you get $\displaystyle \frac{\frac{1}{x}+\frac{1}{x^4}}{1+\frac{1}{x^4}}$ Quote:

3.) limit as x---->2$\displaystyle \frac{\sqrt{x+2}-2}{x-2}$

I think I use the conjugate here.

Well, that is how I tacked the problem. Will post my new answers shortly if I think of a better way to answer them

TIA!

Yes, you would use conjugate here. How did you do with this one?