oblicz granice

[karolcia77]

Prosze o pomoc w rozwiazaniu granic

\(\displaystyle{ \lim_{x\to0} \frac{1-cosx}{e^{x^2}-1}}\)

\(\displaystyle{ \lim_{x\to0}\frac{e^{sin2x}-1}{x}}\)

[tomekture8]

1)\(\displaystyle{ \lim_{ x \to 0} \frac{1-cosx}{e ^{x ^{2} } -1} \stackrel{[H]}{=}\lim_{ x \to 0} \frac{sinx}{2xe ^{x ^{2} } } \stackrel{[H]}{=} \lim_{ x \to 0} \frac{cosx}{2e ^{x ^{2} }+4x ^{2}e ^{x ^{2} } } = \frac{1}{2}}\)


2) \(\displaystyle{ \lim_{ x \to 0} \frac{e ^{sin2x} -1 }{x} \stackrel{[H]}{=} \lim_{ x \to 0} 2e ^{sin2x} cos2x = 2}\)

[karolcia77]

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