Find-lim-x-2-2-sin-4x-1-cos-4x-Find-lim-x-2-sin-6x-1-cos-6x-

Question Number 189757 by Shrinava last updated on 21/Mar/23

Find : \lim_{x \to \frac{π}{2}} \frac{\sqrt{2} ∣ \sin 4 x ∣}{\sqrt{1 - \cos 4 x}} = ?

Find : \lim_{x \to π} \frac{\sqrt{2} ∣ \sin 6 x ∣}{\sqrt{1 - \cos 6 x}} = ?

Answered by Frix last updated on 21/Mar/23

Use t = \tan 2 x in the 1^{st} and t = \tan 3 x in the

2^{nd} with t \to 0 \Rightarrow answer is 2

Answered by mehdee42 last updated on 21/Mar/23

1) l i \underset{x \to \frac{π}{2}}{m} \frac{2 \sqrt{2} ∣ s i n 2 x c o s 2 x ∣}{\sqrt{2} ∣ s i n 2 x ∣} = l i \underset{x \to \frac{π}{2}}{m} 2 ∣ c o s 2 x ∣= 2

2) l i \underset{x \to π}{m} \frac{2 \sqrt{2} ∣ s i n 3 x c o s 3 x ∣}{\sqrt{2} ∣ s i n 3 x ∣} = l i \underset{x \to π}{m} 2 ∣ c o s 3 x ∣= 2

Commented by Shrinava last updated on 24/Mar/23

thank you professor