Resolver limites

por **Jovani Souza** » Ter Out 29, 2013 22:02

Por favor eu gostaria que vocês me ajudassem a resolver os seguintes limites trigonométricos:

a) Lim (sen?x/x-1) com x->1

b) Lim (1-x).tg(?x/2) com x->1

c)Lim (sen2x/?-2x) com x->?/2

d) Lim (cosx-senx/cos2x) com x-> ?/4

e) Lim ((1-cosx).sen²x)/xtg³x com x-> 0

Qualquer uma que vocês resolverem será de grande ajuda.

Obrigado!

por **Man Utd** » Qua Out 30, 2013 10:08

Olá

a)

$\\\\\\ \lim_{x\rightarrow1} \frac{sen(\pi x)}{x-1} \\\\ u=x-1,x\rightarrow1,u\rightarrow0 \\\\\\ \lim_{u\rightarrow 0} \frac{sen(\pi*(u+1))}{u} \\\\\\ \lim_{u\rightarrow 0} \frac{sen(\pi u+\pi))}{u} \\\\\\ \lim_{u\rightarrow 0} \frac{sen(\pi u)*cos(\pi)+sen(\pi)*cos(\pi u)}{u} \\\\\\ \lim_{u\rightarrow 0} -\frac{sen(\pi u)}{u} \\\\ z=\pi*u ,u\rightarrow0,z\rightarrow0 \\\\\\ -\lim_{z\rightarrow 0} \frac{sen(z)}{\frac{z}{\pi}} \\\\\\ -\pi* \lim_{z\rightarrow 0}\frac{senz}{z}=-\pi$

Resolver limites

Resolver limites

Resolver limites

Re: Resolver limites

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