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As it's an indeterminate limit of type $\frac{\infty}{\infty}$, divide both numerator and denominator by the term of the denominator that tends more quickly to infinity (the term that, evaluated at a large value, approaches infinity faster). In this case, that term is
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$\lim_{x\to\infty }\left(\frac{\frac{x^2+4}{e^{\left(2x+1\right)}}}{\frac{5+3e^{\left(2x+1\right)}}{e^{\left(2x+1\right)}}}\right)$
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 infinity. As it's an indeterminate limit of type \frac{\infty}{\infty}, divide both numerator and denominator by the term of the denominator that tends more quickly to infinity (the term that, evaluated at a large value, approaches infinity faster). In this case, that term is . Separate the terms of both fractions. Simplify the fraction . Evaluate the limit \lim_{x\to\infty }\left(\frac{\frac{x^2}{e^{\left(2x+1\right)}}+\frac{4}{e^{\left(2x+1\right)}}}{\frac{5}{e^{\left(2x+1\right)}}+3}\right) by replacing all occurrences of x by \infty .