An object is moving counter-clockwise along a circle with the centre at the origin. At \(t=0\) the object is at point \(A(0,5)\) and at \(t=2\pi\) it is back to point \(A\) for the first time.

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 ...

To construct the tangent to a curve at a certain point A, you draw a line that follows the general direction of the curve at that point. An example of this can be seen below. Once the tangent is ...

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 ...