MCQ
$\lim_{x \rightarrow 0} \frac{{{e}^{{{x}^{2}}}}-\cos x}{{{x}^{2}}}=.......$
- A$\frac{2}{3}$
- B$\frac{1}{3}$
- ✓$\frac{3}{2}$
- Dએક પણ નહીં.
$\lim_{x \rightarrow 0}\frac{{{e}^{{{x}^{2}}}}-\cos x}{{{x}^{2}}}$ $(\frac{0}{0})form$
$=\lim_{x \rightarrow 0}\frac{e^{x^{2}}-1+1-\cos x}{x^2}$
$=\lim_{x \rightarrow 0}\frac{e^{x^{2}}-1}{x^2}+\lim_{x \rightarrow 0}\frac{1-\cos x}{x^2}$
$=1+\lim_{x \rightarrow 0}\frac{\sin x}{2x}$ $(\frac{0}{0})form$
$=1+\lim_{x \rightarrow 0}\frac{\cos x}{2}$
$=1+\frac{1}{2}$
$=\frac{3}{2}$
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