Calculus Examples

$lim_{x \to 8} \frac{π}{2} - \arctan (x) \ln (x)$

Step 1

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

$lim_{x \to 8} \frac{π}{2} - lim_{x \to 8} \arctan (x) \ln (x)$

Step 2

Evaluate the limit of $\frac{π}{2}$ which is constant as $x$ approaches $8$ .

$\frac{π}{2} - lim_{x \to 8} \arctan (x) \ln (x)$

Step 3

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

$\frac{π}{2} - lim_{x \to 8} \arctan (x) \cdot lim_{x \to 8} \ln (x)$

Step 4

Move the limit inside the logarithm.

$\frac{π}{2} - lim_{x \to 8} \arctan (x) \cdot \ln (lim_{x \to 8} x)$

Step 5

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

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Step 5.1

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

$\frac{π}{2} - \arctan (8) \cdot \ln (lim_{x \to 8} x)$

Step 5.2

Evaluate $\arctan (8)$ .

$\frac{π}{2} - 1.44644133 \cdot \ln (lim_{x \to 8} x)$

Step 5.3

Evaluate the limit of $x$ by plugging in $8$ for $x$ .

$\frac{π}{2} - 1.44644133 \cdot \ln (8)$

Step 6

Simplify the answer.

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Step 6.1

Multiply $- 1.44644133$ by $\ln (8)$ .

$\frac{π}{2} - 3.00779019$

Step 6.2

Subtract $3.00779019$ from $\frac{π}{2}$ .

$- 1.43699386$