Math topic中文

Derivative as rate

derivative as rate of change

Practice questions

1In the triangle $ABC$ , $AB = x\ \text{cm}$ , $AC = 3x\ \text{cm}$ and angle $BAC = \dfrac{2\pi}{3}$ . If $x$ is increasing…
2The volume of liquid in a container, $V\ \text{m}^3$ , is given by $V = 0.05\bigl[(3x+2)^3 - 8\bigr],$ where $x$ is the…
3Given that $y = \frac{4}{5}\left(\frac{x}{12} - 1\right)^6$ and that both $x$ and $y$ vary with time, find the value of…
4When the height of liquid in a container is $h$ m, the volume of liquid is $V\text{ m}^3$ where $V = 0.06 \left[ (4h + 1)^3 - 7 \right] \text{ and } h \ge 0.25$ …
5A curve has equation $y = x^2 + x + 2k - 4$ and a line has equation $y - 2x = k$ , where $k$ is a constant. Find the set…
6Cement is poured into an empty right circular cone mould at a constant rate of $36\pi\ \text{cm}^3/\text{s}$ . The height…
7A curve has equation $y = \frac{4}{\sqrt{x+3}}$ . A point $(x, y)$ is moving along the curve. Find the coordinates of the…
8A particle moves in a straight line with a fixed point $O$ . The velocity of the particle, $v$ m/s, is given by $v = \dfrac{25}{2t+1} + 10$ …
9The variables $x$ and $y$ increase in such a way that when $x = 3$ , the rate of increase of $y$ with respect to time is…
10Liquid is poured, at a constant rate of 15 cm $^3$ /s, into a container. When the depth of liquid in the container is $x$ …
11When the hemispherical bowl above contains water to a depth of $x$ cm, the volume, $V\text{ cm}^3$ , of the water is give…