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aev [14]
4 years ago
6

-2x^4 +50x^2+0x-3/x-5

Mathematics
1 answer:
Gemiola [76]4 years ago
3 0
1) "x2" was replaced by "x^2". 1 more similar replacement(s).
Raising zero to a power is not allowed
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Proof in explanation.

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-x^4 \le x^4 \cos(\frac{2}{x}) \le x^4

By squeeze theorem, if  -x^4 \le x^4 \cos(\frac{2}{x}) \le x^4

and \lim_{x \rightarrow 0}-x^4=\lim_{x \rightarrow 0}x^4=L, then we can also conclude that \im_{x \rightarrow} x^4\cos(\frac{2}{x})=L.

So we can actually evaluate the "if" limits pretty easily since both are continuous  and exist at x=0.

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We can finally conclude that \lim_{\rightarrow 0}x^4\cos(\frac{2}{x})=0 by squeeze theorem.

Some people call this sandwich theorem.

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