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Hasil dari
lim_(x rarr oo)(x-2sqrtx)/(sqrtx) adalah..

$1$ . Hasil dari $\lim _{x \rightarrow \infty} \frac{x-2 \sqrt{x}}{\sqrt{x}}$ adalah..

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Evaluate rational exponents

Full solution

Q.

1

. Hasil dari

\lim _{x \rightarrow \infty} \frac{x-2 \sqrt{x}}{\sqrt{x}}

adalah..

Divide by $\sqrt{x}$ : Divide each term in the numerator by $\sqrt{x}$ . $\frac{x}{\sqrt{x}}$ - $\frac{2\sqrt{x}}{\sqrt{x}}$
Simplify terms: Simplify each term. $\sqrt{x} - 2$
Evaluate limits: As $x$ approaches infinity, $\sqrt{x}$ also approaches infinity. $\newline$ So, the limit of $\sqrt{x}$ as $x$ approaches infinity is infinity.
Limit of $\sqrt{x}$ : The limit of $2$ as $x$ approaches infinity is just $2$ , since it's a constant.
Limit of constant: The limit of the expression $(\sqrt{x} - 2)$ as $x$ approaches $\infty$ is $\infty - 2$ , which is still $\infty$ .
Final limit: Therefore, the limit of the original expression $(x - 2\sqrt{x}) / \sqrt{x}$ as $x$ approaches $\infty$ is $\infty$ .

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