Calculus Examples

$lim_{x \to 4.1} \frac{2 - \sqrt{x}}{4 - x}$

Step 1

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $4.1$ .

$\frac{lim_{x \to 4.1} 2 - \sqrt{x}}{lim_{x \to 4.1} 4 - x}$

Step 2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $4.1$ .

$\frac{lim_{x \to 4.1} 2 - lim_{x \to 4.1} \sqrt{x}}{lim_{x \to 4.1} 4 - x}$

Step 3

Evaluate the limit of $2$ which is constant as $x$ approaches $4.1$ .

$\frac{2 - lim_{x \to 4.1} \sqrt{x}}{lim_{x \to 4.1} 4 - x}$

Step 4

Move the limit under the radical sign.

$\frac{2 - \sqrt{lim_{x \to 4.1} x}}{lim_{x \to 4.1} 4 - x}$

Step 5

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $4.1$ .

$\frac{2 - \sqrt{lim_{x \to 4.1} x}}{lim_{x \to 4.1} 4 - lim_{x \to 4.1} x}$

Step 6

Evaluate the limit of $4$ which is constant as $x$ approaches $4.1$ .

$\frac{2 - \sqrt{lim_{x \to 4.1} x}}{4 - lim_{x \to 4.1} x}$

Step 7

Evaluate the limits by plugging in $4.1$ for all occurrences of $x$ .

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Step 7.1

Evaluate the limit of $x$ by plugging in $4.1$ for $x$ .

$\frac{2 - \sqrt{4.1}}{4 - lim_{x \to 4.1} x}$

Step 7.2

Evaluate the limit of $x$ by plugging in $4.1$ for $x$ .

$\frac{2 - \sqrt{4.1}}{4 - 4.1}$

Step 8

Simplify the answer.

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Step 8.1

Subtract $4.1$ from $4$ .

$\frac{2 - \sqrt{4.1}}{- 0.1}$

Step 8.2

Move the negative in front of the fraction.

$- \frac{2 - \sqrt{4.1}}{0.1}$

Step 8.3

Evaluate the root.

$- \frac{2 - 1 \cdot 2.02484567}{0.1}$

Step 8.4

Multiply $- 1$ by $2.02484567$ .

$- \frac{2 - 2.02484567}{0.1}$

Step 8.5

Subtract $2.02484567$ from $2$ .

$- \frac{- 0.02484567}{0.1}$

Step 8.6

Divide $- 0.02484567$ by $0.1$ .

$- - 0.24845673$

Step 8.7

Multiply $- 1$ by $- 0.24845673$ .

$0.24845673$