[" Fita "(x+g)(x+g)cos theta+(y+t)sin theta=kvec wp(f)/(g^(2))(f)/(g^(2))x^(2)+y^(2)+2gx+2fy+c=0" and "(dx)/(dx)(dt)/(dx)]

int x{f(x^(2))g'(x^(2))-f'(x^(2))g(x^(2))}dx

The condition so that the line (x+g)cos theta+(y+f)sin theta=k is a tangent to x^(2)+y^(2)+2gx+2fy+c=0 is

The condition that the line (x + g) cos theta + ( y +f ) sin theta = k is a tangent to x^2+y^2 +2gx +2fy +c=0 :

If x=f(t) and y=g(t), then write the value of (d^(2)y)/(dx^(2))

x=a cos theta+b sin theta and y=a sin theta-b cos theta show that y^(2)(d^(2)y)/(dx^(2))-x(dy)/(dx)+y=0

If x=a cos theta+b sin theta,y=a sin theta-b cos theta then show that y^(2)(d^(2)y)/(dx^(2))-x(dy)/(dx)+y=0

int x{f(x)^(2) g''(x^(2))-f''(x^(2)) g(x^(2))} dx is equal to

If x=a cos theta+b sin theta and y=a sin theta-b cos theta, then prove that y^(2)(d^(2)y)/(dx^(2))-x(dy)/(dx)+y=0

If y = f(x) and x = g(y), where g is the inverse of f, i.e., g = f^(-1) and if (dy)/(dx) and (dx)/(dy) both exist and (dx)/(dy) ne 0 , show that (dy)/(dx) = (1)/((dx//dy)) . Hence, (1) find (d)/(dx) (tan^(-1)x) (2) If y=sin^(-1)x, -1lexle1, -(pi)/(2)leyle(pi)/(2) , then show that (dy)/(dx)=(1)/(sqrt(1-x^(2))) where |x| lt 1 .