limx→ /4 42-cos x+sin x51- sin 2x is equal to (a) 52 (b) 32 (c) 2 - Maths -

Question

lim x → π / 4   4 2 - cos   x + sin   x 5 1
-   sin   2 x is equal to

(a) 5 2

(b)
3 2

(c)
2

(d) none of these

Global Expert · Accepted Answer

(a)

limx→π4 42-cos x+sin x51-sin 2x=limx→π4 252-cos x+sin x2522-1+sin 2x=limx→π4 252-cos x+sin x2522-cos x+sin x2Let t=cos x+sin x2 x→π4∴ t=cos π4+sin π42→22=2=limt→2252-t522-t=52 232                    ∵limx→axn-anx-a=nan-1=52

lim x → π / 4 4 2 - cos x + sin x 5 1 - sin 2 x is equal to (a) 5 2 (b) 3 2 (c) 2 (d) none of these

$\lim_{x \to π / 4} \frac{4 \sqrt{2} - {(\cos x + \sin x)}^{5}}{1 - \sin 2 x}$ is equal to

(a) $5 \sqrt{2}$

(b) $3 \sqrt{2}$

(c) $\sqrt{2}$

(d) none of these