Question

Find the limit as x approaches pi/2 for ((sinx/cos(^2)x)-tan(^2)x)

Answer 1

Since ((sinx/cos^2(x))-tan^2(x)) is continuous at x=pi/2. So you can use \[\lim_{x \rightarrow \pi/2}=f(\pi/2)\]. The answer is 1/2

Answer 2

How do you know that ((sinx/cos^2(x))-tan^2(x)) is continuous at x=pi/2?
If you plug in x=pi/2, then wouldn't it be \[\frac{ 1 }{ 0 } - \frac{ 1 }{ 0 }\]

Answer 3

@KMcc see my steps & answer in the attached picture.