EXERCISE . . Find the slope of the tangent to the following curves at the respective given points. (i) y at x = (ii) x t y at t = π .
. Find the point on the curve y at which the tangent is parallel to the line . Find the points on the curve y where the normal is parallel to the line = . .
Find the points on the curve y + for which the tangent is horizontal. - - Applications of Differential Calculus . Find the tangent and normal to the following curves at the given points on the curve. (i) y at ( , ) (ii) y e x at ( , ) (iii) y at π π (iv) x t y cos , at t = π .
Find the equations of the tangents to the curve y = + for which the tangent is orthogonal with the line x . . Find the equations of the tangents to the curve y which are parallel to the line x . .
Find the equation of tangent and normal to the curve given by x = 7cos and y t t 2sin , at any point on the curve. . Find the angle between the rectangular hyperbola xy = and the parabola x . Show that the two curves x and xy where c r , are constants, cut orthogonally.