Calculus Examples

$lim_{x \to 6} (2 x - 1) \sqrt{x + 4}$

Step 1

Split the limit using the Product of Limits Rule on the limit as $x$ approaches $6$ .

$lim_{x \to 6} 2 x - 1 \cdot lim_{x \to 6} \sqrt{x + 4}$

Step 2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $6$ .

$(lim_{x \to 6} 2 x - lim_{x \to 6} 1) \cdot lim_{x \to 6} \sqrt{x + 4}$

Step 3

Move the term $2$ outside of the limit because it is constant with respect to $x$ .

$(2 lim_{x \to 6} x - lim_{x \to 6} 1) \cdot lim_{x \to 6} \sqrt{x + 4}$

Step 4

Evaluate the limit of $1$ which is constant as $x$ approaches $6$ .

$(2 lim_{x \to 6} x - 1 \cdot 1) \cdot lim_{x \to 6} \sqrt{x + 4}$

Step 5

Move the limit under the radical sign.

$(2 lim_{x \to 6} x - 1 \cdot 1) \cdot \sqrt{lim_{x \to 6} x + 4}$

Step 6

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $6$ .

$(2 lim_{x \to 6} x - 1 \cdot 1) \cdot \sqrt{lim_{x \to 6} x + lim_{x \to 6} 4}$

Step 7

Evaluate the limit of $4$ which is constant as $x$ approaches $6$ .

$(2 lim_{x \to 6} x - 1 \cdot 1) \cdot \sqrt{lim_{x \to 6} x + 4}$

Step 8

Evaluate the limits by plugging in $6$ for all occurrences of $x$ .

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Step 8.1

Evaluate the limit of $x$ by plugging in $6$ for $x$ .

$(2 \cdot 6 - 1 \cdot 1) \cdot \sqrt{lim_{x \to 6} x + 4}$

Step 8.2

Evaluate the limit of $x$ by plugging in $6$ for $x$ .

$(2 \cdot 6 - 1 \cdot 1) \cdot \sqrt{6 + 4}$

Step 9

Simplify the answer.

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Step 9.1

Simplify each term.

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Step 9.1.1

Multiply $2$ by $6$ .

$(12 - 1 \cdot 1) \cdot \sqrt{6 + 4}$

Step 9.1.2

Multiply $- 1$ by $1$ .

$(12 - 1) \cdot \sqrt{6 + 4}$

Step 9.2

Subtract $1$ from $12$ .

$11 \cdot \sqrt{6 + 4}$

Step 9.3

Add $6$ and $4$ .

$11 \sqrt{10}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$11 \sqrt{10}$

Decimal Form:

$34.78505426 \dots$