Calculus Examples

$\frac{lim_{t \to 0} t}{\sqrt{20 t + 16 - 4}}$

Step 1

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

$\frac{0}{\sqrt{20 t + 16 - 4}}$

Step 2

Simplify the answer.

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Step 2.1

Simplify the denominator.

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Step 2.1.1

Subtract $4$ from $16$ .

$\frac{0}{\sqrt{20 t + 12}}$

Step 2.1.2

Factor $4$ out of $20 t + 12$ .

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Step 2.1.2.1

Factor $4$ out of $20 t$ .

$\frac{0}{\sqrt{4 (5 t) + 12}}$

Step 2.1.2.2

Factor $4$ out of $12$ .

$\frac{0}{\sqrt{4 (5 t) + 4 (3)}}$

Step 2.1.2.3

Factor $4$ out of $4 (5 t) + 4 (3)$ .

$\frac{0}{\sqrt{4 (5 t + 3)}}$

$\frac{0}{\sqrt{4 (5 t + 3)}}$

Step 2.1.3

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

$\frac{0}{\sqrt{2^{2} (5 t + 3)}}$

Step 2.1.4

Pull terms out from under the radical.

$\frac{0}{2 \sqrt{5 t + 3}}$

$\frac{0}{2 \sqrt{5 t + 3}}$

Step 2.2

Cancel the common factor of $0$ and $2$ .

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Step 2.2.1

Factor $2$ out of $0$ .

$\frac{2 (0)}{2 \sqrt{5 t + 3}}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $2$ out of $2 \sqrt{5 t + 3}$ .

$\frac{2 (0)}{2 (\sqrt{5 t + 3})}$

Step 2.2.2.2

Cancel the common factor.

$\frac{2 \cdot 0}{2 \sqrt{5 t + 3}}$

Step 2.2.2.3

Rewrite the expression.

$\frac{0}{\sqrt{5 t + 3}}$

$\frac{0}{\sqrt{5 t + 3}}$

$\frac{0}{\sqrt{5 t + 3}}$

Step 2.3

Divide $0$ by $\sqrt{5 t + 3}$ .

$0$

$0$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$