Assignment #2

(Due September 22)

From section 3.2, work problems 6,8,10,12,15,16,18,22,40,41,42,43.

From section 3.3, work problems 1-5, 16-20, 28.  For problems 1-5, calculate the limit not only at infinity, but also at zero.

From section 4.1:

Use the formal limit definition to find the derivatives of  f(x) = x² and g(x)= x³.  When you're done, find the tangent lines to each curve through the point (1,f(1)) and (1,g(1)).

Suppose s(t) tells the position (in meters) of a person as a function of time, t, in seconds.  Sketch a possible graph for s(t) so that the average velocity on the interval [-1,1] is greater than either the instantaneous velocity at t=-1 and the instantaneous velocity at t=1. 

On the previous assignment, we estimated how steep the Mississippi river is based on figures for St. Louis and Memphis.  This was a secant line approximation to the derivative.  Explain what the limit definition of the derivative calculates in common sense, geographical language tailored for this example, and explain what information is produced by calculating the derivative "at Memphis," as opposed to the previous calculation.  The explanations needn't be more than a paragraph or two, and you needn't assemble more data.

Do problems 7,8,27,28,34,60.   In 34 (v), replace "where" with "when."