Calculus Examples

$lim_{x \to 2} \arctan (\frac{4 x^{2} - 16}{7 x^{2} - 14 x})$

Step 1

Simplify the answer.

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Step 1.1

Simplify the denominator.

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Step 1.1.1

Multiply $7$ by $2$ .

$4 \frac{2}{14 - 1 \cdot 7}$

Step 1.1.2

Multiply $- 1$ by $7$ .

$4 \frac{2}{14 - 7}$

Step 1.1.3

Subtract $7$ from $14$ .

$4 (\frac{2}{7})$

Step 1.2

Multiply $4 (\frac{2}{7})$ .

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Step 1.2.1

Combine $4$ and $\frac{2}{7}$ .

$\frac{4 \cdot 2}{7}$

Step 1.2.2

Multiply $4$ by $2$ .

$\frac{8}{7}$

Step 2

Substitute $t$ for $\frac{4 x^{2} - 16}{7 x^{2} - 14 x}$ and let $t$ approach $\frac{8}{7}$ since $lim_{x \to 2} \frac{4 x^{2} - 16}{7 x^{2} - 14 x} = \frac{8}{7}$ .

$lim_{t \to \frac{8}{7}} \arctan (t)$

Step 3

Evaluate the limits by plugging in $\frac{8}{7}$ for all occurrences of $t$ .

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Step 3.1

Simplify the answer.

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Step 3.1.1

Simplify the denominator.

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Step 3.1.1.1

Multiply $7$ by $2$ .

$\arctan (4 \frac{2}{14 - 1 \cdot 7})$

Step 3.1.1.2

Multiply $- 1$ by $7$ .

$\arctan (4 \frac{2}{14 - 7})$

Step 3.1.1.3

Subtract $7$ from $14$ .

$\arctan (4 (\frac{2}{7}))$

Step 3.1.2

Multiply $4 (\frac{2}{7})$ .

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Step 3.1.2.1

Combine $4$ and $\frac{2}{7}$ .

$\arctan (\frac{4 \cdot 2}{7})$

Step 3.1.2.2

Multiply $4$ by $2$ .

$\arctan (\frac{8}{7})$

Step 3.2

Evaluate $\arctan (\frac{8}{7})$ .

$0.85196632$