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 ...

Some have worked out, like snowboarding boots, while others were thankfully abandoned, like Vans’ short-lived Serio line of running shoes from the 1970s. It is hard to imagine an alternate ...

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 ...

As a tangent is a straight line it is described by an equation in the form \(y - b = m(x - a)\). You need both a point and the gradient to find its equation. You are usually given the point - it's ...

Sultry jazz-tinged The Fine Line continues the reflective slant and seems to hark back to some of the first couple of albums.

Construction of the Tangent to a Parabola 2.1 An applet illustrating how the tangent to a parabola is obtained through successive secant lines. Functions with Corners 2.1 Some examples of graphs with ...