1. [V] This question asks you to review your understanding of the geometric meaning of the derivative of a parametrized curve.

(a) Make a sketch of the curve (x, y ) = r(t) = (t^2 , t) for 0 t 2.

(b) Add the vectors r(1), r(1.1), and r(1.1) r(1) to your sketch. [Don't worry about getting the points exactly correct!]

(c) Calculate the tangent vector, r '(1), and add it to your sketch.

(d) Calculate the secant vector (r(1.1) r(1)) / 0.1

add it to your sketch, and explain why it is almost the same as r'(1).