Week 4: June 2 $^$nd - June 8 $^$th

Suggested Problems

Problems you may find instructive, or that I find interesting.

3.1

#7, 15, 21, 25, 27, 34, 35, 37, 40, 41, 50 & 59

(Note that #72 was already suggested, 2.3 #61.)

3.2

#13, 20, 23, 29, 33, 44, 50, 57, 61 & 64

Product Rule is extremely important. If you have time, do as many of #1-44 as you can.

3.3

#19, 29, 35, 39, 53, 55, 61 & 64

(Note that #29 is a lot easier if you split the fraction.)

3.5

#9, 15, 21, 25, 27, 55, 57, 59, 61 & 62

(Question #61 might seem more interesting if compared with 3.6.)

Chain Rule is extrememly important. If you have time, do as many of #1-28 as you can.

3.4

#6, 11(B) & 16

3.6

#7, 9, 19, 24, 28, 29, 33, 41, 47, 53, 58, 61 & 71

(Question #71 is an example of a differential equation.)

3.7

#9, 15, 18, 25, 29, 43, 47 & 58

4.10

#18, 23, 29 & 39

Assigned Problems

Due June 9 $^$th , in lecture.

1. Set
   $$\begin{aligned} g(x) = \left\{\begin{aligned} x, & x \text{ ra... ...\\ 0, & x \text{ irrational}.\end{aligned}\right. \end{aligned}$$

   (a)

   Show that $g$ is not differentiable at 0 .

   (b)

   Show that $p$ is differentiable at 0 , and give $\left.\frac{dp}{dx}\right\vert _{x=0}$ .

   This is 3.1 #52; you might find it helpful to do #59 first.

   Hint: to save writing, recall that in 2.2 we proved the Dirichlet function has no limit.

2. Find the angles at which the circles $(x-1)^2+y^2=10$ and $x^2+(y-2)^2=5$ intersect.

   This is 3.7 #48; you might find it helpful to do #47 first.

3. Calvin's spherical snowball is melting in a way so that the radius changes at a constant rate. When he took the snowball out of the freezer it had a radius of 16cm, but after 30min the radius is 10cm. How fast is the volume of the snowball changing when the radius is 12cm?

   This is 4.10 #14.