" 4."sqrt((a^(2)-x^(2))/(a^(2)+x^(2)))

If =(sqrt(a^(2)+x^(2))+sqrt(a^(2)-x^(2)))/(sqrt(a^(2)+x^(2))-sqrt(a^(2)-x^(2))), show that (dy)/(dx)=(2a^(2))/(x^(3)){1+(a^(2))/(sqrt(a^(4)-x^(4)))}

Let M>0 and L=lim_(x rarr0)(M(1-4sqrt(M^(2)-x^(2))))/(x^(2)sqrt(M^(2)-x^(2))) exists and is a finite non-zero number.Then LM is equal to

THe value of x which satisfy the equation (sqrt(5x^(2)-8x+3))-sqrt((5x^(2)-9x+4))=sqrt((2x^(2)-2x))-sqrt((2x^(2)-3x+1))

Let kgt0 and lambda =lim_(xrarr0) (k(1-4sqrt(k^2-x^2)))/(x^2sqrt(k^2-x^2)) be finite. Then the value of lambdak , is

Let kgt0 and lambda =lim_(xrarr0) (k(1-4sqrt(k^2-x^2)))/(x^2sqrt(k^2-x^2)) be finite. Then the value of lambdak , is

lim_(x rarr sqrt(2))(x^(2)-2)/(x^(2)+sqrt(2)x-4)

If =(sqrt(a^2+x^2)+sqrt(a^2-x^2))/(sqrt(a^2+x^2)-sqrt(a^2-x^2)) , show that (dy)/(dx)=(2a^2)/(x^3){1+(a^2)/(sqrt(a^4-x^4))} .

Evaluate :lim_(x rarr2a^(+))(sqrt(x-2a)+sqrt(x)-sqrt(2a))/(x^(2)-4a^(2))

Solve the equation: (4sqrt((cos x)/(2))-5-(sqrt(2))/(2))^(2)+sqrt(2)(4sqrt((cos x)/(2))-5-(sqrt(2))/(2))-(cos x)/(2)=0