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What Does the Following Mean?
L=lim f(x)
as x approaches A
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Definition
Limit of function is equal to L when x approaches A.
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Term
In this statement, what does "L" represent?
L=lim f(x)
as x approaches A
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Definition
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Term
How do you write:
"x approaches A"
Using Symbols?
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Definition
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Term
How Do You Evaluate This Function?
f(x)=x-A
if
x=B
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Definition
Original Problem:
f(x)=x-A
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Place "B" in Place of "x"
f(B)=B-A
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Solve
B-A
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Term
What Are The Methods For Finding Limits?
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Definition
Method One:
By evaluating the function by using "x" values approaching the "A" value from left to right and from right to left.
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Term
What is the Solution To The Following Problem?
Lim((x^2)+(x-1))
When x -> 3
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Definition
Replace the "x" value for "3" and Evaluate the Function:
((3^2)+(3-1))
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Which Becomes
9+(3-1)
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Which Becomes
9+2
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Which Becomes
11
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The Limit of the Function, and the solution to the problem is:
11
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Term
What is the Solution To The Following Problem?
Lim((x^A)+(x-B))
When x -> C
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Definition
Replace "x" for "D" in the function and Evaluate the Function
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Your Solution is:
((C^A)+(C-B))
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Term
What is the Solution To The Following Problem?
Lim((x+A)/((x^B)-C))
When x -> D
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Definition
Replace "x" for "D" in the function and Evaluate the Function
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Your Solution is:
((D+A)/((D^B)-C))
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Term
What is the Solution to this problem?
A/0
If
A is any real number, not equal to 0
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Definition
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Term
What is the Solution to this problem?
0/A
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Definition
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Term
What is the Solution to this problem?
(A^0)
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Definition
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Term
What is the Solution to this problem?
((A)/(Infinity))
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Definition
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Term
How Do You Factor The Difference of Two Perfect Squares?
(A^2)-(B^2)
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Definition
(A+B)(A-B)
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Term
What is the solution to this problem?
(x+A)/(x-A)(x+A)
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Definition
"(x+A)" in the numerator and the denominator cancel each other out, leaving one as a remainder in the numerator:
1/(x-A)
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The Solution is:
1/(x-A)
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Term
What is the Sum Property of Limits?
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Definition
Lim f(x) + g(x)= Lim f(x) + Lim g(x)
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Term
What is the Difference Property of Limits?
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Definition
Lim f(x) - g(x)= Lim f(x) - Lim g(x)
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Term
What is the Product Property of Limits?
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Definition
Lim f(x) * g(x)= Lim f(x) * Lim g(x)
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Term
What is the Quotient Property of Limits?
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Definition
Lim f(x) / g(x)= Lim f(x) / Lim g(x)
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Term
What is the Power Property of Limits?
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Definition
((Lim f(x))^A) When x -> B
=
(B^A)
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