class 12

Math

Calculus

Application of Derivatives

If p and q are positive real numbers such that $p_{2}+q_{2}=1$, then the maximum value of $(p+q)$ is

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Find the condition if the equation $3x_{2}+4ax+b=0$ has at least one root in $(0,1)˙$

Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height h and semi vertical angle is one-third that of the cone and the greatest volume of cylinder is $274 πh_{3}tan_{2}α˙$

If the tangent at $(1,1)$ on $y_{2}=x(2−x)_{2}$ meets the curve again at $P,$ then find coordinates of $P˙$

In the curve $x_{a}y_{b}=K_{a+b}$ , prove that the potion of the tangent intercepted between the coordinate axes is divided at its points of contact into segments which are in a constant ratio. (All the constants being positive).

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If $1_{0}=α$ radians, then find the approximate value of $cos60_{0}1_{prime}˙$

Let $y=f(x)$ be drawn with $f(0)=2$ and for each real number $a$ the line tangent to $y=f(x)$ at $(a,f(a))$ has x-intercept $(a−2)$. If $f(x)$ is of the form of $ke_{px}$ then$pk $ has the value equal to