We can calculate the gradient of a tangent to a curve by differentiating. In order to find the equation of a tangent, we: Differentiate the equation of the curve Substitute the \(x\) value into ...

As the tangent is a straight line, the equation of the tangent will be of the form \(y = mx + c\). We can use perpendicular gradients to find the value of \(m\), then use the coordinates of P to ...

Over a short time interval \Delta t, This is a statement of the principle of mass conservation for a steady, one-dimensional flow, with one inlet and one outlet. This equation is called the continuity ...

Find \(\ds \lim_{h\to 0}\frac{f(1+h)-f(1)}{h}\) where \(\ds f(x)=\frac{3x+1}{x-2}\text{.}\) What does the result in (a) tell you about the tangent line to the graph ...

Express the polar equation \(r=\cos 2\theta\) in rectangular coordinates. Find the maximum height above the \(x\)-axis of the cardioid \(r=1+\cos \theta\text{.}\) Sketch the graph of the curve whose ...

Read more: iOS 18 Brings These New Features to Your iPhone Here's how to make Messages perform calculations. If you want to ...