= e ln e − e − (1 ln 1 − 1) = e − e − (0 − 1) = 1.
(C) Use the method of partial fractions, letting
Letting x = 0, we find A = 2, and letting x = 3 yields B = −1.
Now
(D) At (2,1), Use Δx = 0.1; then Euler’s method moves to (2.1, 1 +
3(0.1)).
At (2.1, 1.3), so the next point is (2.2, 1.3 + 3.4(0.1)).
(D) Separate variables to get and integrate to get ln y = ln x + C.
Since y = 3 when x = 1, C = ln 3. Then y = e(ln x + ln 3) = e ln x · e ln 3
= 3x.
(D) The generating circle has equation x^2 + y^2 = 4. Using disks, the
volume, V, is given by
(C) The integrals in (A), (B), and (D) all diverge
to infinity.
