True or False? In Exercises 109-114, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. The function f ( x ) = | x − 1 | x − 1 is continuous on ( − ∞ , ∞ ) .
True or False? In Exercises 109-114, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. The function f ( x ) = | x − 1 | x − 1 is continuous on ( − ∞ , ∞ ) .
True or False? In Exercises 109-114, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.
The function
f
(
x
)
=
|
x
−
1
|
x
−
1
is continuous on
(
−
∞
,
∞
)
.
Topic 2
Evaluate S
x
dx, using u-substitution. Then find the integral using
1-x2
trigonometric substitution. Discuss the results!
Topic 3
Explain what an elementary anti-derivative is. Then consider the following
ex
integrals: fed dx
x
1
Sdx
In x
Joseph Liouville proved that the first integral does not have an elementary anti-
derivative Use this fact to prove that the second integral does not have an
elementary anti-derivative. (hint: use an appropriate u-substitution!)
1. Given the vector field F(x, y, z) = -xi, verify the relation
1
V.F(0,0,0) = lim
0+ volume inside Se
ff F• Nds
SE
where SE is the surface enclosing a cube centred at the origin and having edges of length 2€. Then,
determine if the origin is sink or source.
4
3
2
-5 4-3 -2 -1
1 2 3 4 5
12
23
-4
The function graphed above is:
Increasing on the interval(s)
Decreasing on the interval(s)
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