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Midterm

# MATH 1200 Midterm: Review for Midterm 2Premium

3 pages85 viewsFall 2016

Department
Mathematics
Course Code
MATH 1200
Professor
Matthew Demers
Study Guide
Midterm

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Keefer Rourke
November 19, 2016
MATH 1200
Dr. Matt Demers
Calculus midterm 2
Formal deﬁnition of a limit
For any limit limxaf(x) = L, we can deﬁne:
ϵ > 0δ > 0, s.t. if 0<|xa|< δ, then |f(x)L|< ϵ
Limits to inﬁnity
We can construct an argument similar to δϵ, for limits to inﬁnity. The argument is as follows:
case 1:
lim
xaf(x) =
N > 0δ > 0, s.t. if 0<|xa|< δ, then f(x)> N.
where you start with f(x)> N, and work towards 0<|xa|< δ.
Note, if the limit is −∞, then use N < 0.
case 2:
lim
x→∞ f(x) = L
ϵ > 0M > 0s.t. if x > M, then |f(x)L|< ϵ
where you start with f|(x)L|< ϵ, and work towards M > 0.
Note, if approaching −∞, then use x < M and M < 0.
case 3:
lim
x→∞ f(x) =
N > 0M > 0, s.t. if x > M, then f(x)> N.
Note, if approaching −∞, then use x < M and M < 0— if the limit is −∞, then use N < 0.
Intermediate value theorem
If f(x)is continuous on [a, b], then for any y on that interval value, there must be x value that satisﬁes it.
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