The value of limx→0 1+5x21+3x21/x2, is - Infinity Learn by Sri Chaitanya

A
$e^{2}$
B
$e$
C
$e^{- 1}$
D
none of these

Solution:

We have,

$lim_{x \to 0} {(\frac{1 + 5 x^{2}}{1 + 3 x^{2}})}^{\frac{1}{x^{2}}} = e^{lim_{x \to 0} \frac{2 x^{2}}{1 + 3 x^{2}} \cdot \frac{1}{x^{2}}} = e^{{lim_{x \to 0} \frac{2}{1 + 3 x^{2}}}_{}} = e^{2}$ .

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