Calculus Examples

$lim_{x \to 4} 3 x - \sqrt{x}$

Step 1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $4$ .

$lim_{x \to 4} 3 x - lim_{x \to 4} \sqrt{x}$

Step 2

Move the term $3$ outside of the limit because it is constant with respect to $x$ .

$3 lim_{x \to 4} x - lim_{x \to 4} \sqrt{x}$

Step 3

Move the limit under the radical sign.

$3 lim_{x \to 4} x - \sqrt{lim_{x \to 4} x}$

Step 4

Evaluate the limits by plugging in $4$ for all occurrences of $x$ .

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Step 4.1

Evaluate the limit of $x$ by plugging in $4$ for $x$ .

$3 \cdot 4 - \sqrt{lim_{x \to 4} x}$

Step 4.2

Evaluate the limit of $x$ by plugging in $4$ for $x$ .

$3 \cdot 4 - \sqrt{4}$

Step 5

Simplify the answer.

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Step 5.1

Simplify each term.

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Step 5.1.1

Multiply $3$ by $4$ .

$12 - \sqrt{4}$

Step 5.1.2

Rewrite $4$ as $2^{2}$ .

$12 - \sqrt{2^{2}}$

Step 5.1.3

Pull terms out from under the radical, assuming positive real numbers.

$12 - 1 \cdot 2$

Step 5.1.4

Multiply $- 1$ by $2$ .

$12 - 2$

Step 5.2

Subtract $2$ from $12$ .

$10$