help, please ! lim_(x → (𝛑/4)) ((cos((𝛑/4) −x)−tan x)/(1−sin((𝛑/4)+x))) = ???


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Question Number 196107 by maths_plus last updated on 18/Aug/23

$help, please!$ $\underset{x \to \frac{π}{4}}{l i m} \frac{c o s (\frac{π}{4} - x) - t a n x}{1 - s i n (\frac{π}{4} + x)} = ? ? ?$
	Answered by MM42 last updated on 21/Aug/23
	$hop→lim_(x→(π/4)) ((sin((π/4)−x)−(1+tan^2 x))/(−cos((π/4)+x))) =((−2)/0) { ((x→(π^+ /4) =+∞)),((x→(π^− /4) =−∞)) :} ⇒ limit not exist$
	$h o p \to {l i m}_{x \to \frac{π}{4}} \frac{s i n (\frac{π}{4} - x) - (1 + {t a n}^{2} x)}{- c o s (\frac{π}{4} + x)}$ $= \frac{- 2}{0} {\begin{cases} x \to \frac{π^{+}}{4} = + \infty \\ x \to \frac{π^{-}}{4} = - \infty \end{cases}$ $\Rightarrow l i m i t n o t e x i s t$
	Commented by maths_plus last updated on 18/Aug/23

	$thank you$
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