Question

Evaluate : $\underset{x\to \pi }{lim}\frac{1+{\sec }^{3}x}{{\tan }^{2}x}$

Answer 1

$\underset{x\to \pi }{lim}\frac{1+{\sec }^{3}x}{{\tan }^{2}x}$ ($\frac{0}{0}$form)

using L'Hospital rule

$=\underset{x\to \pi }{lim}\frac{3{\sec }^{2}x\sec x\tan x}{2\tan x{\sec }^{2}x}$

$=\underset{x\to \pi }{lim}\frac{3\sec x}{2}$

$=\frac{-3}{2}$