giving .
(D) Use the formula for area in polar coordinates,
then the required area is given by
(See polar graph 63 in the Appendix.)
(C).
(A) The first three derivatives of are , and .
The first four terms of the Maclaurin series (about x = 0) are 1, +2x, + ,
and + . Note also that represents the sum of an infinite geometric
series with first term 1 and common ratio 2x. Hence,
(D) We use parts, first letting u = x^2 , dv = e−xdx; then du = 2x dx, v = −e−x
and
Now we use parts again, letting u = x, dv = e−xdx; then du = dx, v = −e−x
and
Alternatively, we could use the Tic-Tac-Toe Method:
