Calculus Examples

$lim_{x \to 3} \sin^{-1} (\frac{x}{3})$

Step 1

Change the two-sided limit into a left sided limit.

$lim_{x \to 3^{-}} \sin^{-1} (\frac{x}{3})$

Step 2

Evaluate the limits by plugging in $3$ for all occurrences of $x$ .

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Step 2.1

Evaluate the limit of $\sin^{-1} (\frac{x}{3})$ by plugging in $3$ for $x$ .

$\sin^{-1} (\frac{3}{3})$

Step 2.2

Divide $3$ by $3$ .

$\sin^{-1} (1)$

Step 2.3

The exact value of $\sin^{-1} (1)$ is $\frac{π}{2}$ .

$\frac{π}{2}$