Step by step solution to "Evaluate the following limits. limx→π2(x−π2)sec⁡(x)"

chillywilly12a

Answered question

2021-10-21

Evaluate the following limits.

lim_{x \to \frac{π}{2}} (x - \frac{π}{2}) \sec (x)

un4t5o4v

Skilled2021-10-22Added 105 answers

Given,

lim_{x \to \frac{π}{2}} (x - \frac{π}{2}) \sec (x)

On simplification we get

lim_{x \to \frac{π}{2}} (x - \frac{π}{2}) \sec (x) = lim_{x \to \frac{π}{2}} \frac{x - \frac{π}{2}}{\cos x}

lim_{x \to \frac{π}{2}} \frac{1 - 0}{(- \sin x)}

lim_{x \to \frac{π}{2}} \frac{- 1}{\sin x}

= \frac{- 1}{\frac{\sin π}{2}}

= \frac{- 1}{1}

= - 1

Jeffrey Jordon

Expert2022-08-30Added 2605 answers

Answer is given below (on video)

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