represent its Cartesian coordinates \((x,y)\) in terms of \(\theta\text{.}\) Find the slope of the tangent line to the curve where \(\ds \theta = \frac{\pi }{2}\text{.}\) Find the points on this curve ...

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 ...

the tangent line touches the curve at a single point the tangent line has the same gradient (slope) as the curve at this point Use tangents at different times to determine the rate of reaction at ...

To construct the tangent to a curve at a certain point A, you draw a line that follows the general ... to remember that all lines and curves that slope upwards have a positive gradient.