Write-ups of the problems below are due Monday Nov. 13

Monday Nov. 6

Topics: 7.4, 7.5
Read the Example of Sec. 7.5, staring at the bottom of p. 328.
Solve, write-up and turn in:  Sec. 7.4: 3, 7, 18 where take the formula for the parabola y for granted and solve (a), (b).
                                                 Sec. 7.5:  1, 3, 5, 11
Tuesday Nov. 7

Topics: 7.6
Solve, write-up and turn in:  Sec. 7.6: 1, 3, 7, 9, 11. Bonus: 12.

Wednesday Nov. 8

8.2, start 8.4
Solve, write-up and turn in:  1. We defined ln x for x>0 by  ln(x) = the definite integral, from 1 to x, of 1/t dt.
                                                      What about the definite integral of 1/t dt on an interval included in the negative x-axis? Show that
                                                      the integral, from -1 to x (where x<0),  of 1/t dt  equals   ln|x|+a constant.

                                                  2.  Using the definition of ln(x) as the definite integral, from 1 to x, of 1/t dt show that  ln(1/x)=-ln(x).
            Hint: substitute t=s/x (s is the new variable of integration).

                                                  3.  Furthermore, show that ln(xy)=ln(x)+ln(y).
            Hint: substitute t=sy (s is the new variable of integration) and use 2. above.

Thursday Nov. 9

8.2-8.4, review the inverse of a function
For Exam II: you need to know the graph and properties of ln(x) and of exp(x), and to integrate and differentiate these functions.
Solve: Sec. 8.4: 1e-o,
Solve, write-up and turn in:  Sec. 8.3: 1, 3 , 11, 15, 19, 24, 25, 27
                                                  Sec. 8.4: 1a,b,c,d, 2a,b,c, 3a, 5a, b,k, 17
Solve for review (you do not need to turn them in): Sec. 8.4: 8-12

Review topics for Exam II
Related rates
Integration by substitution (5.3)
Differential equations (5.4)
Area under the graph of a positive function. Riemann sums.
Definition of a Riemann integrable function on [a,b].
Theorem: a continuous function on a closed interval is Riemann integrable.
Simple examples of functions not continuous, yet integrable.
The definite integral of f(x) on [a,b] (the Riemann integral) is the area between the graph of f and the segment [a,b] with sign.
Calculation of areas as limits of Riemann sums.
And the other way around: calculation of limits of sums noting that they are Riemann sums.
The Fundamental Theorem of Calculus.
Properties of definite integrals.
Area between two curves.
Volumes of solids of revolution: disk (or washer) method, cylindrical shells method.
Volumes by integrating the areas of the cross-sections.
Arc length.
Area of a surface of revolution.
e^x and ln: they are inverse to each other, limits for e, their domains, range, derivatives, graphs,
integrating 1/x, and  e^x  (as such or in combination with substitutions)

Make sure you know how to solve all the assigned homework problems.

Monday Nov. 13
Tuesday Nov. 14 Exam II