Math 171 — Calculus I
Spring 2016
Name:
Weekly Write-Up on Sections 2.4-2.6
Problem 1.
From the suggested homework:
(x + a)3 − a3
x→0
x
[2.5 #53] Evaluate in terms of the constant a. lim
Problem 2. From an old exam:
The gravitational force exerted by the Earth on a unit mass at a distance r from the center of the planet
is given by
GM
if r ≥ R
F (r) = 2
r
where M is the mass of the Earth, R is its radius, and G is the universal gravitational constant. It is
also know that for r < R, the force is directly proportional to the distance from the center of the planet.
In other words
F (r) = Cr for 0 ≤ r < R
for some constant C. Find the constant C in terms of M ,G, and R so that the force is continuous at
r = R. You need to use the definition of continuity to justify your answer.
1
2
Problem 3. For in-class discussion:
Consider the unit circle:
A
C
θ
O
Determine the following limits:
(a) lim
θ→0
area of sector AOB
area of ∆ AOD
area of sector AOB
θ→0
area of ∆ AOB
(b) lim
(c) lim
length of segment AB
length of segment CB
(d) lim
length of segment AB
length of segment AD
θ→0
θ→0
D
B