question_answer 1)

Find the equations of the tangent and normal to the given curves at the indicated points :       (I)   y = x4 ? 6x3 + 13x2 ? 10x + 5 at (0, 5)       (II)   y = x4 ? 6x3 + 13x2 ? 10x + 5 at (1, 3)       (III)  y = x3 at (1, 1)       (IV) y = x2 at (0, 0)       (V)  x = cos t, y = sin t at t  

Answer:

(I) Given curve is             y = x4 ? 6x3 + 13x2 ? 10x + 5      ? (1)                         m =slope of tangent to (1)                         Equation of tangent to (1) at (0, 50) is             y ? y1= m (x ? x1)                         m = slope of tangent to (1)                         Equation of tangent to (1) at (0, 5) is             y ? y1 = m (x ? x1)                                     and equation of normal to (1) at (0, 5) is                                                  10y ? 50 = x        x ? 10y + 50 = 0.       (II) Given curve is       y = x4 ? 6x3 + 13x2 ? 10x + 5 ?. (1)             m = slope of tangent to (1) at (1, 3)              Equation of tangent to (1) at (1, 3) is       y ? 3 = 2 (x ? 1)             Equation of normal to (1) at (1, 3) is                         (III) Given curve is             y = x3             m = slope of tangent to (1)             = 3(1)2 = 3        Equation of tangent to (1) at (1, 1) is       y ? 1 = 3 (x ? 1)       Equation of normal to (1) at (1, 1) is                         (IV) Given curve is       y = x2             m = slope of tangent to (1) at (0, 0)              Equation of tangent to (1) at origin is             y ? 0 = 0 (x ? 0)       y = 0       Equation of normal to (1) at origin is       y ? 0 =                   (V)  Given curve is             x = cos t and y = sin t       When       and         lies on the curve.       Now                   m = slope of tangent to the given curve              Equation of tangent to given curve at  is.              and equation of normal to given curve is