Calculus Examples

$lim_{θ \to \frac{π}{2}} \frac{1}{3} \tan (θ)$

Step 1

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

$lim_{θ \to {(\frac{π}{2})}^{+}} \frac{1}{3} \tan (θ)$

Step 2

Since the function $\tan (θ)$ approaches $- \infty$ , the positive constant $\frac{1}{3}$ times the function also approaches $- \infty$ .

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Step 2.1

Consider the limit with the constant multiple $\frac{1}{3}$ removed.

$lim_{θ \to {(\frac{π}{2})}^{+}} \tan (θ)$

Step 2.2

As the $θ$ values approach $\frac{π}{2}$ from the right, the function values decrease without bound.

$- \infty$