Evaluate $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \sqrt[x^3]{1-x+\sin{x}}}$

Evaluate $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{2^x-1}{\sqrt{1+x}-1}}$

Evaluate $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize {\Bigg(\dfrac{5x^2+1}{3x^2+1}\Bigg)}^\dfrac{1}{x^2}}$

Evaluate $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{5^x+5^{-x}-2}{x^2}}$

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