Question

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

• 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)

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