(UFF)Cálculo de Limites
Enviado: Sex 11 Mar, 2016 19:51
Calcule o seguinte limite.
[tex3]\lim x\rightarrow 0^{+}[/tex3] [tex3]x^{sen(x)}[/tex3]
[tex3]\lim x\rightarrow 0^{+}[/tex3] [tex3]x^{sen(x)}[/tex3]
- Código: Selecionar tudo
[tex3]\lim_{x \to 0^+} x^{\sin x} = \exp (\lim_{ x \to 0^+} \sin x \ln x ) = \exp (\lim_{x\to0^+} \frac{\ln x}{\csc x}) \\ \exp(\lim_{x\to0^+} \frac{\ln x}{\csc x} ) = \exp (\lim_{ x \to 0^+} \frac{1}{x \cdot (- \csc x \cdot \cot x )} ) = \exp (\lim_{x \to 0^+} \frac{\sin x \cdot \tan x}{x}) \\ \exp (\lim_{ x \to 0^+} \frac{\sin x}{x} \cdot \lim_{ x \to 0^+} \tan x ) = \exp (1\cdot 0) = \exp (0) = e^0 = 1 \\ \therefore \lim_{ x \to 0^+} x^{\sin x} = 1[/tex3]