Calculus Examples

$lim_{x \to 8} \arctan (x^{6} - x^{8})$

Step 1

Simplify the answer.

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Step 1.1

Simplify each term.

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Step 1.1.1

Raise $8$ to the power of $6$ .

$262144 - 8^{8}$

Step 1.1.2

Raise $8$ to the power of $8$ .

$262144 - 1 \cdot 16777216$

Step 1.1.3

Multiply $- 1$ by $16777216$ .

$262144 - 16777216$

Step 1.2

Subtract $16777216$ from $262144$ .

$- 16515072$

Step 2

Substitute $t$ for $x^{6} - x^{8}$ and let $t$ approach $- 16515072$ since $lim_{x \to 8} x^{6} - x^{8} = - 16515072$ .

$lim_{t \to - 16515072} \arctan (t)$

Step 3

Evaluate the limits by plugging in $- 16515072$ for all occurrences of $t$ .

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Step 3.1

Simplify the answer.

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Step 3.1.1

Simplify each term.

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Step 3.1.1.1

Raise $8$ to the power of $6$ .

$\arctan (262144 - 8^{8})$

Step 3.1.1.2

Raise $8$ to the power of $8$ .

$\arctan (262144 - 1 \cdot 16777216)$

Step 3.1.1.3

Multiply $- 1$ by $16777216$ .

$\arctan (262144 - 16777216)$

Step 3.1.2

Subtract $16777216$ from $262144$ .

$\arctan (- 16515072)$

Step 3.2

Evaluate $\arctan (- 16515072)$ .

$- \frac{π}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{π}{2}$

Decimal Form:

$- 1.57079632 \dots$