Chapter 1: Q. 16 (page 153)

Consider the limit expression
$\lim_{x \to 4} \frac{2 - \sqrt{x}}{4 - x}$
Calculate the limit.

Short Answer

Expert verified

The limit of the expression is $\infty .$

Step by step solution

Step 1. Given

The given expression is

$\lim_{x \to 4} \frac{2 - \sqrt{x}}{4 - x}$

Step 2. Calculation

The evaluated expression is

$\lim_{x \to 4} \frac{2 - \sqrt{x}}{4 - x} = \frac{\lim_{x \to 4} (2 - \sqrt{x})}{\lim_{x \to 4} (4 - x)} [Quotient rule] = \frac{\lim_{x \to 4} (2) - \lim_{x \to 4} (\sqrt{x})}{\lim_{x \to 4} (4) - \lim_{x \to 4} (x)} [Difference Rule] = \frac{2 - \sqrt{4}}{4 - 4} = \frac{2 - 2}{0} = \infty$

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Consider the limit expression
$\lim_{x \to 4} \frac{2 - \sqrt{x}}{4 - x}$
Calculate the limit.

Short Answer

Step by step solution

Step 1. Given

Step 2. Calculation

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Consider the limit expression
$\lim_{x \to 4} \frac{2 - \sqrt{x}}{4 - x}$
Calculate the limit.