Prove that `underset(xrarrinfty)Lim(x^2+ax+b)/(x^2+cx+d)` is a number independent of a ,b,c and d.

If (x-a)^2 + (y-b)^2 = c^2 , for some c > 0 , prove that [1+(dy/dx)^2]^(3/2)/((d^2y)/dx^2) is a constant independent of a and b.

If underset(xtooo)lim((x^(2)+x+1)/(x+1)-ax-b)=4, then

Differentiate (ax+b)/(cx+d) w.r.t x.

lim_(x rarr 1)(ax^(2)+bx+c)/(cx^(2)+bx+a), a+b+c ne 0 is :

Let f: R rarr R be a positive increasing function with underset(xrarrinfty)lim(f(3x))/(f(x))=1, then underset(xrarrinfty)lim(f(2x))/(f(x)) =

If (a+bx)/(a-bx) =(b+cx)/(b-cx) =(c + dx)/(c-dx) (x ne 0) , then show that a,b,c and d are G.P.

Evaluate the following integrals: int (ax+b)/(cx+d) dx .

Find the derivative of (ax + b)(cx + d)^2 , where a,b,c and d are non zero constants .

Evaluate the given limit : lim_(x to 0) (ax + b)/(cx + 1)