Hii !
I don't know Calculat This Limits :
1. $\displaystyle \lim_{x \to 1^+ } \frac{\sqrt{x^2-9} + \sqrt{x} - \sqrt{3}}{\sqrt{x-3} }$
2. $\displaystyle \lim_{x \to \frac{\Pi }{4}} \frac{1 -\sqrt{2}\cos x}{ 1-\sqrt{2}\sin x }$
Can You Help Me
Hii !
I don't know Calculat This Limits :
1. $\displaystyle \lim_{x \to 1^+ } \frac{\sqrt{x^2-9} + \sqrt{x} - \sqrt{3}}{\sqrt{x-3} }$
2. $\displaystyle \lim_{x \to \frac{\Pi }{4}} \frac{1 -\sqrt{2}\cos x}{ 1-\sqrt{2}\sin x }$
Can You Help Me
$\displaystyle x=1$ is a point at which the expression is continuous so just substitute $\displaystyle x=1$ and evaluate (it is complex).
L'Hopital's rule:2. $\displaystyle \lim_{x \to \frac{\Pi }{4}} \frac{1 -\sqrt{2}\cos x}{ 1-\sqrt{2}\sin x }$
$\displaystyle \lim_{x \to \frac{\pi }{4}} \frac{1 -\sqrt{2}\cos (x)}{ 1-\sqrt{2}\sin (x) }=\lim_{x \to \frac{\pi }{4}} \frac{+\sqrt{2}\sin (x)}{ -\sqrt{2}\cos (x) }$
CB