Math 171 — Calculus I Spring 2016
Name:
1
Weekly Write-Up on Sections 2.1-2.3
Problem 1.
From the suggested homework:
[2.2 #53] Sketch the graph of the function with the given limits.
lim f (x) = f (2) = 3, lim− f (x) = −1, lim f (x) = 2 6= f (4).
x→2+
Problem 2.
x→4
x→2
From an old exam:
The fungus Fusarium exosporium infects a field of flax plants through the roots and
causes the plants to wilt. Eventually, the entire field is infected. The percentage f (t)
of infected plants as a function of time t (in days) since planting is shown in the figure
below.
a. What are the units
of the rate of change
of f (t) with respect
to t?
b. Which
interval
[0, 10], [20, 30], or
[40, 50] has the
largest average infection rate?
Circle one:
[0, 10] [20, 30] [40, 50]
c. Which
interval
[0, 10], [20, 30], or
[40, 50] has the
smallest
average
infection rate?
Circle one:
[0, 10] [20, 30] [40, 50]
2
Problem 3.
For in-class discussion:
Light waves of frequency λ passing through a slit of width a produce a Fraunhofer
diffraction pattern of light and dark fringes (see figure). The intensity as a function of
the angle θ is
2
sin(R sin θ)
I(θ) = Im
R sin θ
where R = πa/λ and Im is a constant.
Show that the intensity function is not defined at θ = 0.
Then choose any two positive values for R check numerically that I(θ) approached Im
as θ → 0.
±1
±.1
±.01
±.001
±.0001
R=
θ
I(θ)
θ
I(θ)
±1
±.1
±.01
±.001
±.0001
R=