" 15."(x+1)/(sqrt(x^(2)+1))

(1)/(sqrt(15+4x-4x^(2)))

If 2x = sqrt(a) - (1)/(sqrt(a)) , then the value of (sqrt(x^(2) + 1))/(x + sqrt(x^(2) +1)) is

If x+sqrt(x^(2)-1)+(1)/(x+sqrt(x^(2)+1))=20 then x^(2)+sqrt(x^(4)-1)+(1)/(x^(2)+sqrt(x^(4)-1))=

lim_(x rarr1)(sqrt(x^(2)-1)+sqrt(x-1))/(sqrt(x^(2)-1))

Evaluate lim_(x rarr 1) (sqrt(x^(2)-1)+sqrt(x-1))/(sqrt(x^(2)-1))

Differentiate (sqrt(x^(2)+1)+sqrt(x^(2)-1))/(sqrt(x^(2)+1)-sqrt(x^(2)-1)) with respect to x:

If x=(1)/(2)(sqrt(a)+(1)/(sqrt(a))) , then show that (sqrt(x^(2)-1))/(x-sqrt(x^(2)-1))=(a-1)/(2) .

Integrate (8)/(sqrt(1-(4x)^(2)))+(27)/(sqrt(1-9x^(2)))-(15)/(1+25x^(2)) with respect to x .

(8)/(sqrt(1 - (4 x)^(2))) + (27)/(sqrt(1 - 9 x^(2))) - (15)/(1+ 25 x^(2))

(d)/(dx)[cos^(-1)(x sqrt(x)-sqrt((1-x)(1-x^(2))))]=(1)/(sqrt(1-x^(2)))-(1)/(2sqrt(x-x^(2)))(-1)/(sqrt(1-x^(2)))-(1)/(2sqrt(x-x^(2)))(1)/(sqrt(1-x^(2)))+(1)/(2sqrt(x-x^(2)))(1)/(sqrt(1-x^(2)))0 b.1/4c.-1/4d none of these