# Have Fun with Limits

**Calculus**Level 4

\[\large \lim_{x\rightarrow 0}\frac{\frac{x^{2}}{2}+1-\sqrt{1+x^{2}}}{(\cos{(x)}-e^{x^{2}})\sin (x^{2})} = \ ? \]

Give your answer to 3 significant figures.

\[\large \lim_{x\rightarrow 0}\frac{\frac{x^{2}}{2}+1-\sqrt{1+x^{2}}}{(\cos{(x)}-e^{x^{2}})\sin (x^{2})} = \ ? \]

Give your answer to 3 significant figures.

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