1. Warm Up No Calculator A curve is described by the parametric equations
x = t2 + 2t, y = t3 + t2. An equation of the line tangent to the curve at the point where t = 1 is
3) A particle moves along the x-axis so that at any time t > 0 the acceleration of the particle is a(t) = e-2t . If at t = 0 the velocity of the particle is 5/2 and its position is 17/4, then its position at any time t > 0 is x(t) =

2. Graphing Polar curves without a calculator

3. Use your calculator to make generalizations… Graph various values of each scalar (a, b and n), then generalize. 1.
a) r = a b) r = acos θ c) r = asin θ
Generalizations that will help you graph each without a calculator:

4. These are called “cardioids”
2. a) r = a  b cos θ b) r = a  b sin θ If a = b, generalizations that will help you graph without a calculator…
These are called “cardioids”

5. 2. a) r = a  bcos θ b) r = a  bsin θ
If a < b, generalizations that will help you graph without a calculator…
These are called “limaçons”

6. 2. a) r = a  bcos θ b) r = a  bsin θ
If a > b, generalizations that will help you graph without a calculator…
These are called “limaçons with an inner loop”

7. 3. a) r = acos(nθ) b) r = asin(nθ)
If n is an odd number, generalizations that will help you graph without a calculator…
If n is an even number, generalizations that will help you graph without a calculator…
These are called “rose curves”

12. Where do the graphs intersect?

13. Where do the graphs intersect?