[tex]\lim_{x\to 0} x*ctg2x[/tex]решите пж лимит. Created by lepme. algebra-ru

tex]решите пж лимит...

армения20171

Замена бесконечно малых эквивалентными:

$\lim\limits _{x \to 0}\, (x\cdot ctg2x)=\lim\limits _{x \to 0}\frac{x}{tg2x}=\Big [\; tg\alpha \sim \alpha\; ,\; esli\; \alpha \to 0\; ;\; \alpha =2x\to 0\; \Big ]=\\\\=\lim\limits _{x \to 0}\frac{x}{2x}=\frac{1}{2}$

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NNNLLL54

Verified answer

Lim(x*ctg2x)
x->0

=lim(x*(cos²x-sin²x)/2sinx*cosx=
=lim(x*(ctgx-tgx)/2=
lim(x*ctgx-x*tgx)/2=
lim(x/tgx-x*tgx)/2=
lim(x-xtg²x)/2tgx

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Answers & Comments

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