Final Answer
$e^{6}$
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Step-by-step Solution
Problem to solve:
$\lim_{x\to\infty}\left(1+\frac{3}{x}\right)^{2x}$
Specify the solving method
1
Rewrite the limit using the identity: $a^x=e^{x\ln\left(a\right)}$
$\lim_{x\to\infty }\left(e^{2x\ln\left(1+\frac{3}{x}\right)}\right)$
Learn how to solve limits to infinity problems step by step online.
$\lim_{x\to\infty }\left(e^{2x\ln\left(1+\frac{3}{x}\right)}\right)$
Learn how to solve limits to infinity problems step by step online. Find the limit of (1+3/x)^(2x) as x approaches \infty. Rewrite the limit using the identity: a^x=e^{x\ln\left(a\right)}. Apply the power rule of limits: \displaystyle{\lim_{x\to a}f(x)^{g(x)} = \lim_{x\to a}f(x)^{\displaystyle\lim_{x\to a}g(x)}}. The limit of a constant is just the constant. Rewrite the product inside the limit as a fraction.
Final Answer
$e^{6}$
Numeric Answer
$403.428793$