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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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$\lim_{x\to\infty }\left(\frac{\frac{x^2e^x}{e^{3x}}}{\frac{1+e^{3x}}{e^{3x}}}\right)$
Learn how to solve problems step by step online. Find the limit of (x^2e^x)/(1+e^(3x)) 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 . The quotient of powers of same base (\frac{x^2e^x}{e^{3x}}) can be rewritten as the base to the power of the difference of the exponents.