Calculus Examples

$lim_{x \to 8} \arctan (x) - \arctan (1)$

Step 1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $8$ .

$lim_{x \to 8} \arctan (x) - lim_{x \to 8} \arctan (1)$

Step 2

Evaluate the limit of $\arctan (1)$ which is constant as $x$ approaches $8$ .

$lim_{x \to 8} \arctan (x) - \arctan (1)$

Step 3

Evaluate the limits by plugging in $8$ for all occurrences of $x$ .

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Step 3.1

Evaluate the limit of $\arctan (x)$ by plugging in $8$ for $x$ .

$\arctan (8) - \arctan (1)$

Step 3.2

Evaluate $\arctan (8)$ .

$1.44644133 - \arctan (1)$

Step 4

Simplify the answer.

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Step 4.1

The exact value of $\arctan (1)$ is $\frac{π}{4}$ .

$1.44644133 - \frac{π}{4}$

Step 4.2

Subtract $\frac{π}{4}$ from $1.44644133$ .

$0.66104316$