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Calc Midterm 1
Induction; Sufficiently Close; Limits; Continuity
10
Mathematics
Undergraduate 1
10/23/2013

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Cards

Term
What is the Def of a Limit?
Definition

 Let f(x) be a function defined on an interval that contains [image][image][image][image], except possibly at [image][image][image][image].  Then we say that,

[image][image][image][image]

if for every number [image][image][image][image] there is some number [image][image][image][image] such that

[image][image][image]

Term
Defintion of Sufficiently Close?
Definition
For a property P of real numbers x suffieciently close to c means there is a Δ such all x with o<|x-c|<Δ have property P.
Term
What is the definition of a limit using suffienctly close numbers?
Definition

[image] if only for all Ε>0 for all suffiecently close to c |f(x)-L| <Ε

P is the property |f(x)-L| <Ε

Term
True or False: All polynomials are continuous?
Definition
True
Term
How do you find the limit of f(x)/g(x)?
Definition
[image]
Term
How do you find the limit of a function mulitplied by a constant?
Definition
[image]
Term
How do you find the limit of two functions being added together?
Definition
[image];
Term
How do you solve for a limit of two functions multiplied together?
Definition
[image].
Term
What is the equation for an odd function?
Definition
f(–x) = –f(x)
Term
What is the equation for an even function?
Definition
f(–x) = f(x)
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