Question

Lim x-π (x-π) tan x/2. Find limit.

Answer 1

❏Question :-

$\displaystyle \lim_{x \to \pi} \: (x - \pi) \: \tan \big(\frac{x}{2} \big)$

❏Answer :-

$\boxed{ \displaystyle \lim_{x \to \pi} \: (x - \pi) \: \tan \big(\frac{x}{2} \big) = 0} \:$

❏Used property :-

$\star \: \boxed{\displaystyle \lim\sf \frac{ \tan h}{h} = 1}$

❏Solution :-

We Have

$\to\displaystyle \lim_{x \to \pi} \: (x - \pi) \: \tan \big( \frac{x}{2} \big)\: \\ \\ \to \: \displaystyle \lim_{x \to \pi} \: (x - \pi) \: \tan \big(\frac{x}{2} \big) \times \frac{ \big( \frac{x}{2} \big)}{ \big( \frac{x}{2} \big) } \\ \\ \to \: \displaystyle \lim_{x \to \pi} \: \frac{x}{2} (x - \pi) \: \frac{ \tan \big( \frac{x}{2} \big)}{ \big( \frac{x}{2} \big)} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \because \: \boxed{\displaystyle \lim\sf \frac{ \tan h}{h} = 1} \: \\ \therefore \\ \to \: \displaystyle \lim_{x \to \pi} \: \frac{x}{2} (x - \pi) \: \: \\ \\ \to \: \displaystyle \lim_{x \to \pi} \: \frac{ {x}^{2} }{2} - \frac{x}{2} \pi \: \\ \mathbb{ \red{TAKING} \: \: LIMIT \: } \\ \\ \to \frac{ { \pi}^{2} }{2} - \frac{ \pi}{2} \times \pi \\ \\ \to \: \frac{ { \pi}^{2} }{2} - \frac{ { \pi}^{2} }{2} \\ \\ \boxed{ \displaystyle \lim_{x \to \pi} \: (x - \pi) \: \tan \big(\frac{x}{2} \big) = 0}$

Answer 2

Answer:0

Step-by-step explanation:

The other answer has a mistake

Because - lim (tan h)/h = 1 is true when lim h----->0 but it is not the case in the question

For correct answer u can refer the picture