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(1)[tex] \lim_{x\rightarrow -\infty} \frac{x-2}{x^{2} + 2x + 1} [/tex]. I factored it as [tex] \frac{x-2}{(x+1)^{2}} [/tex]. Then what?

(2) [tex] \lim_{x\rightarrow -\infty} \frac{\sqrt{5x^{2}-2}}{x+3} [/tex]. For this one would I just multiply both sides by the numerator? I am not sure what to do with this one.

(3) [tex] \lim_{x\rightarrow -\infty} \frac{\sqrt{3x^{4}+x}}{x^{2}-8} [/tex]. Would I do the same thing and multiply both sides by the numerator?

(4) [tex] \lim_{x\rightarrow 3} \frac{x}{x-3} [/tex]. Is there any way I can separate this?

(5) [tex] \lim_{x\rightarrow 4-} \frac{3-x}{x^{2}-2x-8} [/tex]. Would I just factor both the numerator and denominator?

(6) [tex] \lim_{x\rightarrow\infty} \frac{7-6x^{5}}{x+3} [/tex]. For this one would I also factor? Not sure how to do it.

(7)[tex] \lim_{x\rightarrow 0-} \frac{x}{|x|} [/tex]. This would just be -1?

(8) [tex] \lim_{x\rightarrow 0} \frac{\sin 2\theta}{\theta^{2}} [/tex]. This wouldnt exist? [tex] \frac{\sin 2\theta}{\theta^{2}} = 2\cos\theta(\frac{\sin\theta}{\theta})(\frac{1}{\theta}) [/tex]. How would I show this algebraically?

Thanks

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# Homework Help: Limits and Derivatives

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