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 ...

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 the ...

Elastic flows and gradient flows in planar curves form a vibrant area of research in geometric analysis, where curves evolve in time under rules dictated by an energy functional. Central to this ...

The yield spread between long-term and short-term Treasury securities is known to be a good predictor of economic activity, particularly of looming recessions. One way to learn more is through a ...