Exercises

01

Find the equation of the tangent line to the parametric curve $(x,y)=(t^2+1,t^3-4t)$ at the point given by $t=3$. Where is the tangent line horizontal?

02

Find an integral formula for the length of the circumference of a general ellipse (centered at the origin). (Do not try to evaluate the integral!)

03

Suppose a particle traces the graph of a parabola with its position given parametrically by $(x,y)=(t,t^2)$. How fast is the particle moving at time $t=10$? What is its acceleration at $t=10$?

04

Compute the curvature function $\kappa (t)$ for the circle given parametrically by $(r\cos (t),r\sin (t))$. Is the answer what you should have expected?