Calculus Examples

$lim_{x \to 3.8} \frac{2 - \sqrt{x}}{4 - x}$

Step 1

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $3.8$ .

$\frac{lim_{x \to 3.8} 2 - \sqrt{x}}{lim_{x \to 3.8} 4 - x}$

Step 2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $3.8$ .

$\frac{lim_{x \to 3.8} 2 - lim_{x \to 3.8} \sqrt{x}}{lim_{x \to 3.8} 4 - x}$

Step 3

Evaluate the limit of $2$ which is constant as $x$ approaches $3.8$ .

$\frac{2 - lim_{x \to 3.8} \sqrt{x}}{lim_{x \to 3.8} 4 - x}$

Step 4

Move the limit under the radical sign.

$\frac{2 - \sqrt{lim_{x \to 3.8} x}}{lim_{x \to 3.8} 4 - x}$

Step 5

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $3.8$ .

$\frac{2 - \sqrt{lim_{x \to 3.8} x}}{lim_{x \to 3.8} 4 - lim_{x \to 3.8} x}$

Step 6

Evaluate the limit of $4$ which is constant as $x$ approaches $3.8$ .

$\frac{2 - \sqrt{lim_{x \to 3.8} x}}{4 - lim_{x \to 3.8} x}$

Step 7

Evaluate the limits by plugging in $3.8$ for all occurrences of $x$ .

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Step 7.1

Evaluate the limit of $x$ by plugging in $3.8$ for $x$ .

$\frac{2 - \sqrt{3.8}}{4 - lim_{x \to 3.8} x}$

Step 7.2

Evaluate the limit of $x$ by plugging in $3.8$ for $x$ .

$\frac{2 - \sqrt{3.8}}{4 - 3.8}$

Step 8

Simplify the answer.

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Step 8.1

Subtract $3.8$ from $4$ .

$\frac{2 - \sqrt{3.8}}{0.2}$

Step 8.2

Evaluate the root.

$\frac{2 - 1 \cdot 1.94935886}{0.2}$

Step 8.3

Multiply $- 1$ by $1.94935886$ .

$\frac{2 - 1.94935886}{0.2}$

Step 8.4

Subtract $1.94935886$ from $2$ .

$\frac{0.05064113}{0.2}$

Step 8.5

Divide $0.05064113$ by $0.2$ .

$0.25320565$