`(1+sqrt(x))/(1-sqrt(x))`

Evaluate int(1)/(sqrt(x))(sqrt(x)+(1)/(sqrt(x)))^(2)dx

Differentiate tan^(-1)((sqrt(x)+sqrt(a))/(1-sqrt(x a))) with respect to x

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

lim_(xrarr0) (sqrt(1+x^2)- sqrt(1+x))/(sqrt(1+x^3)-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))

int_(0)^(1)(1)/(sqrt(1+x)-sqrt(x))dx

Differentiate the following with respect to x\ :tan^(-1)\ ((sqrt(1+x)\ \ -\ \ sqrt(1-x))/(sqrt(1+x\ \ )+\ \ sqrt(1-x)))\

Prove that tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))=pi/4-1/2cos^(-1)x,-1/(sqrt(2))lt=xlt=1

Prove that tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)-sqrt(1-x)))=pi/4-1/2cos^(-1),-1/(sqrt(2))lt=xlt=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