Calculus Examples

$lim_{x \to 8} \arccos (\frac{1 + x^{2}}{1 + 2 x^{2}})$

Step 1

Evaluate the limit of $\arccos (\frac{1 + x^{2}}{1 + 2 x^{2}})$ by plugging in $8$ for $x$ .

$\arccos (\frac{1 + 8^{2}}{1 + 2 \cdot 8^{2}})$

Step 2

Simplify the numerator.

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Step 2.1

Raise $8$ to the power of $2$ .

$\arccos (\frac{1 + 64}{1 + 2 \cdot 8^{2}})$

Step 2.2

Add $1$ and $64$ .

$\arccos (\frac{65}{1 + 2 \cdot 8^{2}})$

Step 3

Simplify the denominator.

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Step 3.1

Raise $8$ to the power of $2$ .

$\arccos (\frac{65}{1 + 2 \cdot 64})$

Step 3.2

Multiply $2$ by $64$ .

$\arccos (\frac{65}{1 + 128})$

Step 3.3

Add $1$ and $128$ .

$\arccos (\frac{65}{129})$

Step 4

Evaluate $\arccos (\frac{65}{129})$ .

$1.04271615$