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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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$\lim_{x\to\infty }\left(\frac{\frac{\sqrt{9+2x}-5}{\sqrt[3]{x}}}{\frac{\sqrt[3]{x}-2}{\sqrt[3]{x}}}\right)$
Learn how to solve problems step by step online. Find the limit of ((9+2x)^(1/2)-5)/(x^(1/3)-2) 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 . Rewrite the fraction, in such a way that both numerator and denominator are inside the exponent or radical. Separate the terms of both fractions. Simplify the fraction \frac{\frac{x}{\left(\sqrt{9+2x}-5\right)^{3}}}{\frac{x}{\left(\sqrt[3]{x}-2\right)^{3}}}.
