lim(x->0)(x+2sinx)/(sqrt(x^2+2sinx+1)-sq...

`lim_(x->0)(x+2sinx)/(sqrt(x^2+2sinx+1)-sqrt(sin^2x-x+1))`

Verified by Experts

The correct Answer is:

2

`lim_(xto0)((x/x+(2 sin x)/x)(sqrt(x^(2)+2sinx+1)+sqrt(sin^(2)x-x+1)))/((x^(2))/x-(sin^(2)x)/x+(2 sinx)/x+x/x)=2`

Similar Questions

Explore conceptually related problems

lim_(x rarr0)(x+2sin x)/(sqrt(x^(2)+2sin x+1)-sqrt(sin^(2)x-x+1))

lim_(x to 0) (x +2 sin x)/(sqrt(x^(2)+2 sin x + 1)-sqrt(sin^(2) x - x+ 1)) is

lim_(xto0)(sin2x)/(1-sqrt(1-x))

lim_(x rarr0)(sin^(2)x)/(sqrt(2)-sqrt(1+cos x))

lim_(xrarr0)(sinx)/(sqrt(x+1)-sqrt(1-x)) is equal to

lim_(x rarr 0) (sqrt(1+sinx)-sqrt(1-sinx))/x=

Show that : cot^(-1) [(sqrt(1 + sinx) + sqrt(1 - sinx))/(sqrt(1 + sinx) - sqrt(1 - sinx))]= x/2

cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=(x)/(2), x in (0,(pi)/(4))