Calculus Examples

$lim_{x \to 4} 2^{x} + \sqrt{x} - x$

Step 1

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

$lim_{x \to 4} 2^{x} + lim_{x \to 4} \sqrt{x} - lim_{x \to 4} x$

Step 2

Move the limit into the exponent.

$2^{lim_{x \to 4} x} + lim_{x \to 4} \sqrt{x} - lim_{x \to 4} x$

Step 3

Move the limit under the radical sign.

$2^{lim_{x \to 4} x} + \sqrt{lim_{x \to 4} x} - lim_{x \to 4} x$

Step 4

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

Tap for more steps...

Step 4.1

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

$2^{4} + \sqrt{lim_{x \to 4} x} - lim_{x \to 4} x$

Step 4.2

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

$2^{4} + \sqrt{4} - lim_{x \to 4} x$

Step 4.3

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

$2^{4} + \sqrt{4} - 4$

Step 5

Simplify the answer.

Tap for more steps...

Step 5.1

Simplify each term.

Tap for more steps...

Step 5.1.1

Raise $2$ to the power of $4$ .

$16 + \sqrt{4} - 4$

Step 5.1.2

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

$16 + \sqrt{2^{2}} - 4$

Step 5.1.3

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

$16 + 2 - 4$

Step 5.2

Add $16$ and $2$ .

$18 - 4$

Step 5.3

Subtract $4$ from $18$ .

$14$