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1. \(\displaystyle{ \lim_{x \to0 }}\)\(\displaystyle{ \frac{arctg2x}{arctg3x}}\)

2. \(\displaystyle{ \lim_{x \to 0 ^{+} }}\)\(\displaystyle{ \left( sinx\right) ^{x}}\)

3. \(\displaystyle{ \lim_{ x\to \infty }}\)\(\displaystyle{ \left(4 ^{ \frac{1}{x} }-3 ^{ \frac{1}{x} } \right)}\)

1. \(\displaystyle{ \lim_{x \to0 }}\)\(\displaystyle{ \frac{arctg2x}{arctg3x}}\)

\(\displaystyle{ tgx= \frac{sinx}{cosx}}\)

2. \(\displaystyle{ \lim_{x \to 0 ^{+} }}\)\(\displaystyle{ \left( sinx\right) ^{x}=1}\)

3. \(\displaystyle{ \lim_{ x\to \infty }}\)\(\displaystyle{ \left(4 ^{ \frac{1}{x} }-3 ^{ \frac{1}{x} } \right) = \lim_{ x\to \infty } \sqrt[x]{4} - \lim_{ x\to \infty } \sqrt[x]{3} =1-1=0}\)

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