find the limit. (if the limit is infinite, enter ∞ or -∞, as appropriate. if the limit \n lim _ { x…

find the limit. (if the limit is infinite, enter ∞ or -∞, as appropriate. if the limit \n lim _ { x \rightarrow infty } \frac { 36 - sqrt { x } } { 6 + sqrt { x } }

find the limit. (if the limit is infinite, enter ∞ or -∞, as appropriate. if the limit \n lim _ { x \rightarrow infty } \frac { 36 - sqrt { x } } { 6 + sqrt { x } }

Answer

Explanation:

Step1: Divide numerator and denominator by $\sqrt{x}$

$$\lim_{x\rightarrow\infty}\frac{\frac{36}{\sqrt{x}} - 1}{\frac{6}{\sqrt{x}}+1}$$

Step2: Use the limit property $\lim_{x\rightarrow\infty}\frac{c}{\sqrt{x}} = 0$ ($c$ is a constant)

As $x\rightarrow\infty$, $\lim_{x\rightarrow\infty}\frac{36}{\sqrt{x}}=0$ and $\lim_{x\rightarrow\infty}\frac{6}{\sqrt{x}} = 0$. So the limit becomes $\frac{0 - 1}{0 + 1}$.

Answer:

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