Question

Assertion: $\displaystyle \lim _{x \rightarrow 0}(1+3 x)^{1 / x}=e^{3}$.
Reason: Since $\displaystyle \lim _{x \rightarrow 0}(1+x)^{1 / x}=e$.

• A. Assertion is correct, reason is correct; reason is a correct explanation for assertion
• B. Assertion is correct, reason is correct; reason is not a correct explanation for assertion
• C. Assertion is correct, reason is incorrect
• D. Assertion is incorrect, reason is correct

Answer 1

Answer: (A)

$\displaystyle \lim _{x \rightarrow 0}(1+3 x)^{1 / x}=\displaystyle \lim _{x \rightarrow 0}\left[\left(1+3 x^{1 / 3 x}\right)\right]^{3}=e^{3}$
because $\displaystyle \lim _{x \rightarrow 0}(1+x)^{1 / x}=e$