Applications of Differentiation

2018 MI Promo Q11 The diagram shows an empty double-walled drinking glass. Both the inner and outer walls are made of ceramic glass in the shape of an open cylinder

2018 HCI Promo Q2 [It is given that the arc length of a circle is $rtheta $, where $r$ is the radius of the circle and $theta $ is the

2018 RI Promo Q2 An equilateral triangle with sides of length $a$ cm is used to construct the base of a triangular prism container of height $36$ cm (see Fig.

2022 VJC J1 MYE Q6 A curve $C$ has parametric equations $x=t-{{tan }^{-1}}left( 2t-1 right)$, $y=2t+1$, for $-2le tle 3$. (i) Show that $frac{text{d}y}{text{d}x}=2left[ frac{{{left( 2t-1 right)}^{2}}+1}{{{left( 2t-1 right)}^{2}}-1} right]$.

2018 EJC Promo Q10 A curve $C$ has equation $5{{y}^{2}}-3xy+3{{x}^{2}}-48=0$, with $yge 0$. $C$ cuts the $x$-axis at points $P$ and $R$. (i) The point $Qleft( x,y right)$ lies on

2018 AJC Promo Q5 A curve $C$ has equation ${{x}^{2}}-xy+{{y}^{2}}-alpha =0$, where $alpha $ is a positive real number. (i) Show that $left( 2y-x right)frac{text{d}y}{text{d}x}=y-2x$. [1] (ii) It is given