Chapter 4.04: Indeterminate Forms and L'Hospital's Rule

QA: Is the "s" in l'Hospital silent, or is it pronounced?

2
4
8
11
14 (be sure to graph both the numerator and denominator separately first--
it's important to see how x^2 is shaped sort of like 1-cos(x) )
19
24 (graph it on [1,10] first, then on [1,100] )
25 why is this one important? The numerator is e^x - (1+x), and 1+x is the
tangent line to e^x at a=0. So e^x - (1+x) is the gap between e^x and a
simple approximation of e^x. Start by graphing e^x - (1+x) on [-2,2] and
then also x^2 on the same graph.

26 Similar to #25, we're looking at the gap between a function and its
tangent line approximation. sinh(x) can be computed as follows:
sinh(x) = (e^x  -  e^-x) / 2

29 Graph both the numerator and denominator first.
30
42 I just saw a function like this in a math/chemistry project in Math 319.
45 Related to the "skewness of the Normal distribution" in prob/stat. 
Not that you need to know that to do the problem.

48 WEP
61 note that x^(1/x) is the x'th root of x--that's what makes this problem
interesting.
67
71 & 72: Everyone should read the problems; math & math-ed majors should
actually prove them.

76 WEP 
77
78 WEP
87 (note: why don't we use this as the definition of derivative? because
it doesn't actually include the value at f(x), which seems like it should
be important when talking about the rate of change at x)

88 WEP

QB: the function sinc(x)=sin(pi* x) / (pi*x) is important in signal
processing, radar images, etc.; it is pronounced "sink".
i) graph sinc(x) from -3 to 3.
ii) Find lim (x->0) sinc(x).