Calculus Examples

$lim_{x \to 8} \frac{1}{\frac{π}{2} - \arctan (x)} - \frac{1}{\arcsin (\frac{1}{x})}$

Step 1

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

$lim_{x \to 8} \frac{1}{\frac{π}{2} - \arctan (x)} - lim_{x \to 8} \frac{1}{\arcsin (\frac{1}{x})}$

Step 2

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

$\frac{lim_{x \to 8} 1}{lim_{x \to 8} \frac{π}{2} - \arctan (x)} - lim_{x \to 8} \frac{1}{\arcsin (\frac{1}{x})}$

Step 3

Evaluate the limit of $1$ which is constant as $x$ approaches $8$ .

$\frac{1}{lim_{x \to 8} \frac{π}{2} - \arctan (x)} - lim_{x \to 8} \frac{1}{\arcsin (\frac{1}{x})}$

Step 4

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

$\frac{1}{lim_{x \to 8} \frac{π}{2} - lim_{x \to 8} \arctan (x)} - lim_{x \to 8} \frac{1}{\arcsin (\frac{1}{x})}$

Step 5

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

$\frac{1}{\frac{π}{2} - lim_{x \to 8} \arctan (x)} - lim_{x \to 8} \frac{1}{\arcsin (\frac{1}{x})}$

Step 6

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

$\frac{1}{\frac{π}{2} - lim_{x \to 8} \arctan (x)} - \frac{lim_{x \to 8} 1}{lim_{x \to 8} \arcsin (\frac{1}{x})}$

Step 7

Evaluate the limit of $1$ which is constant as $x$ approaches $8$ .

$\frac{1}{\frac{π}{2} - lim_{x \to 8} \arctan (x)} - \frac{1}{lim_{x \to 8} \arcsin (\frac{1}{x})}$

Step 8

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

Tap for more steps...

Step 8.1

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

$\frac{1}{\frac{π}{2} - \arctan (8)} - \frac{1}{lim_{x \to 8} \arcsin (\frac{1}{x})}$

Step 8.2

Evaluate $\arctan (8)$ .

$\frac{1}{\frac{π}{2} - 1.44644133} - \frac{1}{lim_{x \to 8} \arcsin (\frac{1}{x})}$

Step 8.3

Evaluate the limit of $\arcsin (\frac{1}{x})$ by plugging in $8$ for $x$ .

$\frac{1}{\frac{π}{2} - 1.44644133} - \frac{1}{\arcsin (\frac{1}{8})}$

Step 8.4

Evaluate $\arcsin (\frac{1}{8})$ .

$\frac{1}{\frac{π}{2} - 1.44644133} - \frac{1}{0.12532783}$

Step 9

Simplify the answer.

Tap for more steps...

Step 9.1

Simplify each term.

Tap for more steps...

Step 9.1.1

Subtract $1.44644133$ from $\frac{π}{2}$ .

$\frac{1}{0.12435499} - \frac{1}{0.12532783}$

Step 9.1.2

Divide $1$ by $0.12435499$ .

$8.04149446 - \frac{1}{0.12532783}$

Step 9.1.3

Divide $1$ by $0.12532783$ .

$8.04149446 - 1 \cdot 7.97907368$

Step 9.1.4

Multiply $- 1$ by $7.97907368$ .

$8.04149446 - 7.97907368$

Step 9.2

Subtract $7.97907368$ from $8.04149446$ .

$0.06242077$