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$$1) \lim_{x\rightarrow\infty} \frac {5}{\frac{1}{x^2}-1}+\lim_{x \rightarrow \infty}2^{\frac{1}{x}}=-5+1=-4$$

$$2) \lim_{x \rightarrow \infty} \frac {3+\frac{1}{x}}{\sqrt{3+\frac{1}{x^2}}}=\frac{3}{\sqrt3}=...$$

$$ 3) \lim_{x \rightarrow 2} \frac {sin(x-2)}{(x-2)}\cdot \lim_{x \rightarrow 2}\frac {1}{x+2}+\lim_{x \rightarrow 2}2^{-\frac{1}{(x-2)^2}}=1\cdot 1/4+0=...$$

$$4)\lim_{x \rightarrow 0} \frac{sin^2x(\sqrt{1+xsinx}+cosx)}{1+xsinx-cos^2x} =\lim_{x \rightarrow 0} \frac{sin^2x(\sqrt{1+xsinx}+cosx)}{sin^2x+xsinx}= $$

$$=\lim_{x \rightarrow 0} \frac{sinx(\sqrt{1+xsinx}+cosx)}{sinx+x}= \lim_{x \rightarrow 0} \frac{\frac{sinx}{x}(\sqrt{1+xsinx}+cosx)}{\frac{sinx}{x}+1}=...$$