Calculus Examples

$lim_{x \to 0} \sqrt{7 + s e^{2} (x)}$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit under the radical sign.

$\sqrt{lim_{x \to 0} 7 + s e^{2} (x)}$

Step 1.2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $0$ .

$\sqrt{lim_{x \to 0} 7 + lim_{x \to 0} s e^{2} (x)}$

Step 1.3

Evaluate the limit of $7$ which is constant as $x$ approaches $0$ .

$\sqrt{7 + lim_{x \to 0} s e^{2} (x)}$

Step 1.4

Move the term $s e^{2}$ outside of the limit because it is constant with respect to $x$ .

$\sqrt{7 + s e^{2} lim_{x \to 0} x}$

Step 2

Evaluate the limit of $x$ by plugging in $0$ for $x$ .

$\sqrt{7 + s e^{2} \cdot 0}$

Step 3

Simplify the answer.

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Step 3.1

Factor $7$ out of $7 + s e^{2} \cdot 0$ .

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Step 3.1.1

Factor $7$ out of $7$ .

$\sqrt{7 (1) + s e^{2} \cdot 0}$

Step 3.1.2

Factor $7$ out of $s e^{2} \cdot 0$ .

$\sqrt{7 (1) + 7 (s e^{2} \cdot 0)}$

Step 3.1.3

Factor $7$ out of $7 (1) + 7 (s e^{2} \cdot 0)$ .

$\sqrt{7 (1 + s e^{2} \cdot 0)}$

Step 3.2

Multiply $s e^{2} \cdot 0$ .

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Step 3.2.1

Multiply $0$ by $s$ .

$\sqrt{7 (1 + 0 e^{2})}$

Step 3.2.2

Multiply $0$ by $e^{2}$ .

$\sqrt{7 (1 + 0)}$

Step 3.3

Add $1$ and $0$ .

$\sqrt{7 \cdot 1}$

Step 3.4

Multiply $7$ by $1$ .

$\sqrt{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{7}$

Decimal Form:

$2.64575131 \dots$