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AP ICET 2024 6th May 2024 Shift 1

Question : 186 of 200

Marks: +1, -0

\lim\limits_{x\to\infty}5\left(1+\frac{4}{x}\right)^x=

Solution:

Solution:

We recognize that the expression

\left(1+\frac{4}{x}\right)^x

is a form of the limit definition of the exponential function

e

. As

x\to\infty

, we have:

\lim\limits_{x\to\infty}\left(1+\frac{4}{x}\right)^x=e^4

Thus, the limit becomes:

\lim\limits_{x\to\infty}5\left(1+\frac{4}{x}\right)^x=5e^4

Quick Tip

Recognize the standard limit form

\left(1+\frac{a}{x}\right)^x

as it approaches

e^a

x\to\infty

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