$ \lim _{x \rightarrow 0}\left\{(1+x)^{\frac{2}{x}}\right\} $ (where $ \{.\} $ denotes the fractional part of $ x $ ) is equal to

Question

$ \lim _{x \rightarrow 0}\left\{(1+x)^{\frac{2}{x}}\right\} $ (where $ \{.\} $ denotes the fractional part of $ x $ ) is equal to, $ e^{2}-7 $, $ e^{2}-8 $, $ e^{2}-6 $, None of these

MARKS App · Accepted Answer

We know, 1 + x 2 / x = 1 + x 2 / x - 1 + x 2 / x Also, lim x → 0 1 + x 2 / x = e 2 ⇒ lim x → 0 1 + x 2 / x = lim x → 0 1 + x 2 / x - lim x → 0 1 + x 2 / x = e 2 - e 2 = e 2 - 7

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