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Exercise

$\lim\:_{x\to\:+\infty\:}\left(\frac{x-2}{x+3}\right)^{-\frac{1}{2}x}$

Step-by-step Solution

1

Evaluate the limit $\lim_{x\to+\infty}\left(\left(\frac{x-2}{x+3}\right)^{-\frac{1}{2}x}\right)$ by replacing all occurrences of $x$ by $+\infty$

$\left(\frac{+\infty-2}{+\infty+3}\right)^{-\frac{1}{2}\cdot +\infty}$

Final answer to the exercise

$\left(\frac{+\infty-2}{+\infty+3}\right)^{-\frac{1}{2}\cdot +\infty}$

Try other ways to solve this exercise

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  • Solve using limit properties
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  • Integrate by partial fractions
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Main Topic: Limits of Exponential Functions

Those are limits of expressions of the form f(x)^g(x).

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