" 15."quad sqrt(4-sqrt(1-x))-sqrt(2-x)>0

sqrt(x+1)-sqrt(x-1)=sqrt(4x-1)

the equation is sqrt(x+3-4sqrt(x-1))+sqrt(x+15-8sqrt(x-1))=2 has:

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

underset(x to 0)"Lt" (sqrt(1-x)-sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1+x))=

Evaluate the following limits : Lim_(x to 0 ) (sqrt(1+x)-sqrt(1+x^(2)))/(sqrt(1-x^(2))-sqrt(1-x))

If y = tan^(-1) ((sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))) show that (dy)/(dx) = x/sqrt(1-x^4) .

Prove that: tan^(-1){(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))}=pi/4-1/2. cos^(-1)x , 0

Prove that: tan^(-1){(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))}=pi/4-1/2. cos^(-1)x , 0 < x < 1

Prove that: tan^(-1){(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))}=pi/4-1/2 cos^(-1)x , 0

Find Lt_(xto0)(sqrt(1+x)-sqrt(1+x^(2)))/(sqrt(1-x^(2))-sqrt(1-x))