1. a) Find the 7^th degree MacLaurin polynomial for the function f(x)=ln(1+x).

b) Use your approximation from part a to estimate ln(1.1) and ln(3).
 

2. a) Graph the 7^th and 8^th degree Maclaurin polynomials for f(x)=ln(1+x) together with f(x).

b) Explain clearly in a few sentences why your estimates in problem 1b were as accurate or inaccurate as they were.

c) Would using a higher degree MacLaurin polynomial improve the situation?
 

3. Consider the family of curves whose parametric equations are x(t)=t², y(t)=t³-ct.

a) Describe how the shape of the curves varies with the value of c.

b) Find (possibly in terms of c) the values of t and coordinates (x,y) of all places on the graph where the tangent line is horizontal.

c) Find (possibly in terms of c) the slope(s) of the curves at their x-intercept(s).
 

4. For the family of curves in problem 3, find the area "inside" the loop, if any, in terms of the value of c.
 

5. Do problem #30 from Stewart section 9.1, p. 552.
 

6. Approximate the length of one cycle of the trochoid from problem 5,

a) for r=10 and d=5.

b) for r=10 and d=15.