class 12

Math

Calculus

Application of Derivatives

The normal to the curve $y(x−2)(x−3)=x+6$at the point where the curve intersects the y-axis ,passes through the point :$(21 ,−31 )$ (2) $(21 ,31 )$ (3) $(−21 ,−21 )$ (4) $(21 ,21 )$

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Find the approximate change in the surface area of a cube of side x metres caused by decreasing the side by 1%.

Find the point on the curve $y=(x−2)_{2}$ at which the tangent is parallel to the chord joining the points (2,0) and (4,4).

Find the equations of the tangent and normal to the hyperbola $a_{2}x_{2} −b_{2}y_{2} =1$. at the point $(x_{0},y_{0})$

If the radius of a sphere is measured as 9 m with an error of 0.03 m, then find the approximate error in calculating its surface area.

Find the equation of tangent to the curve given by$x=asin_{3}t,y=bcos_{3}t$ ... (1)at a point where $t=2π $.

The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference?

Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is $34r $.

Find the intervals in which the function f given by $f(x)=2x_{3}−3x_{2}−36x+7$is (a) strictly increasing (b) strictly decreasing