Class 12

Math

Calculus

Application of Derivatives

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.

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Separate the intervals of monotonocity of the function: $f(x)=−sin_{3}x+3sin_{2}x+5,x∈[−2π ,2π ]˙$

The two curves $x_{3}−3xy_{2}+2=0$ and $3x_{2}y−y_{3}−2=0$

If the tangent to the curve $xy+ax+by=0$ at $(1,1)$ is inclined at an angle $tan_{−1}2$ with x-axis, then find $aandb?$

Find the approximate value of $(26)_{31}$ .

Find the angle between the curves $2y_{2}=x_{3}andy_{2}=32x˙$

$f(x)=∣ax−b∣+c∣x∣∀x∈(−∞,∞),$ where $a>0,b>0,c>0.$ Find the condition if $f(x)$ attains the minimum value only at one point.

Find the angle of intersection of $y=a_{x}andy=b_{x}$

A horse runs along a circle with a speed of $20km/h$ . A lantern is at the centre of the circle. A fence is along the tangent to the circle at the point at which the horse starts. Find the speed with which the shadow of the horse moves along the fence at the moment when it covers 1/8 of the circle in km/h.