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# Find the limit of $\frac{x^2+4}{5+3e^{\left(2x+1\right)}}$ as $x$ approaches $\infty$

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## Step-by-step Solution

Problem to solve:

$\lim_{x\to+\infty}\left(\frac{X^2+4}{5+3e^{2x+1}}\right)$

Specify the solving method

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Apply the property of the product of two powers of the same base in reverse: $a^{m+n}=a^m\cdot a^n$

$\lim_{x\to\infty }\left(\frac{x^2+4}{5+3ee^{2x}}\right)$

Learn how to solve limits to infinity problems step by step online.

$\lim_{x\to\infty }\left(\frac{x^2+4}{5+3ee^{2x}}\right)$

Learn how to solve limits to infinity problems step by step online. Find the limit of (x^2+4)/(5+3e^(2x+1)) as x approaches \infty. Apply the property of the product of two powers of the same base in reverse: a^{m+n}=a^m\cdot a^n. If we directly evaluate the limit \lim_{x\to \infty }\left(\frac{x^2+4}{5+3ee^{2x}}\right) as x tends to \infty , we can see that it gives us an indeterminate form. We can solve this limit by applying L'Hôpital's rule, which consists of calculating the derivative of both the numerator and the denominator separately. After deriving both the numerator and denominator, the limit results in.

$\lim_{x\to+\infty}\left(\frac{X^2+4}{5+3e^{2x+1}}\right)$