Calculus Examples

$lim_{x \to 8} (4) \arctan (\frac{x}{3})$

Step 1

Move the term $4$ outside of the limit because it is constant with respect to $x$ .

$4 lim_{x \to 8} \arctan (\frac{x}{3})$

Step 2

Combine $\frac{1}{3}$ and $8$ .

$4 (\frac{8}{3})$

Step 3

Substitute $t$ for $\frac{x}{3}$ and let $t$ approach $\frac{8}{3}$ since $lim_{x \to 8} \frac{x}{3} = \frac{8}{3}$ .

$4 lim_{t \to \frac{8}{3}} \arctan (t)$

Step 4

Evaluate the limits by plugging in $\frac{8}{3}$ for all occurrences of $t$ .

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Step 4.1

Combine $\frac{1}{3}$ and $8$ .

$4 \arctan (\frac{8}{3})$

Step 4.2

Evaluate $\arctan (\frac{8}{3})$ .

$4 \cdot 1.21202565$

Step 5

Multiply $4$ by $1.21202565$ .

$4.84810262$