At the point `P(a,a^(n))` on the graph of `y=x^(n),(n in N),` in the first quadrant, a normal is drwn. The normal intersects the y-axis at the point `(0,b)If lim _(ato0) b=1/2,` then n equal

If y = n^x, n > 0 then dy/dx is equal to

Let y=f(x) be a curve passing through (4,3) such that slope of normal at any point lying in the first quadrant is negative and the normal and tangent at any point P cuts the Y-axis at A and B respectively such that the mid-point of AB is origin, then the number of solutions of y=f(x) and y=|5-|x||, is

Find the equations of the tangent and normal to the hyperbola x^2/a^2 - y^2/b^2 = 1 at the point (x_0,y_0)

Find the angle of intersection of y=a^xa n dy=b^x

The tangent to the hyperbola xy=c^2 at the point P intersects the x-axis at T and y- axis at T'.The normal to the hyperbola at P intersects the x-axis at N and the y-axis at N' . The areas of the triangles PNT and PN'T' are Delta and Delta' respectively, then 1/Delta+1/(Delta)' is

The ordinates of points P and Q on the parabola y^2 = 12x are in the ratio 1 : 2. Find the locus of the point of intersection of the normals to the parabola at P and Q.