Podcast
Questions and Answers
What is the limit of a constant C as x approaches a?
What is the limit of a constant C as x approaches a?
- a
- C (correct)
- 1
- 0
What is the limit of x as x approaches a?
What is the limit of x as x approaches a?
- 1
- 0
- a (correct)
- x
The limit of a constant times a function is equal to?
The limit of a constant times a function is equal to?
- The constant plus the limit of the function.
- The limit of the function raised to the power of the constant.
- The constant divided by the limit of the function.
- The constant times the limit of the function. (correct)
When finding the limit of f(x) + g(x) as x approaches a, what can you do?
When finding the limit of f(x) + g(x) as x approaches a, what can you do?
What is the limit of [f(x)]^n as x approaches a?
What is the limit of [f(x)]^n as x approaches a?
What is the limit of sqrt[n](f(x)) as x approaches a?
What is the limit of sqrt[n](f(x)) as x approaches a?
If lim x->c f(x) = f(c), what does this indicate?
If lim x->c f(x) = f(c), what does this indicate?
What is the limit of the constant 4 as x approaches 2?
What is the limit of the constant 4 as x approaches 2?
What is the limit of x as x approaches 5?
What is the limit of x as x approaches 5?
Given the limit of 4x as x approaches 2, and given the constant multiple rule, what is the first step?
Given the limit of 4x as x approaches 2, and given the constant multiple rule, what is the first step?
What is lim x+7 as x approaches 2?
What is lim x+7 as x approaches 2?
What is lim 3 * (2x+1) as x approaches 2?
What is lim 3 * (2x+1) as x approaches 2?
What is lim (2x+5) / (x+3) as x approaches 2?
What is lim (2x+5) / (x+3) as x approaches 2?
What is lim (3x+4)^3 as x approaches 1?
What is lim (3x+4)^3 as x approaches 1?
What is lim sqrt(x^2 + 4) as x approaches 2?
What is lim sqrt(x^2 + 4) as x approaches 2?
What is lim (2x-8) as x approaches 5?
What is lim (2x-8) as x approaches 5?
Flashcards
Limit of a Constant
Limit of a Constant
The limit of a constant C as x approaches a is C.
Limit of Identity
Limit of Identity
The limit of x as x approaches a is a.
Limit of Constant Times a Function
Limit of Constant Times a Function
The limit of a constant times a function is equal to the constant times the limit of the function
Limit of a Sum
Limit of a Sum
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Limit of a Difference
Limit of a Difference
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Limit of a Product
Limit of a Product
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Limit of a Quotient
Limit of a Quotient
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Limit of a Power
Limit of a Power
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Limit of a Root
Limit of a Root
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Limit of a Function
Limit of a Function
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Study Notes
Limit Laws
-
lim C = C, illustrates The Law of Constant
- Ex: lim d = 4 = 4
- x->2
-
lim x = a demonstrates the Law of Identity
- Ex: lim x = 5 = 5
- x->5
-
lim c * F(x) = c lim F(x) depicts a limit of a constant c times a function which results in the constant times the limit of the function
- Ex: lim 4x = 4 * lim x = 4(2) = 8
- x->2
-
lim [F(x) + g(x)] = lim F(x) + lim g(x)
- Ex: lim x + 7 = lim x + lim 7 = 2 + 7 = 9
- x->2
-
lim [F(x) - g(x)] = lim F(x) - lim g(x)
- Ex: lim x - 5 = lim x - lim 5 = 3 - 5 = -2
- x->3
-
lim [F(x) * g(x)] = lim F(x) * lim g(x), substitute the value of x at the end
- Ex: lim 3(2x+1) = lim 3 * lim (2x+1) = 3 * [2(2)+1] = 15
- x->2
-
lim [F(x) / g(x)] = lim F(x) / lim g(x)
- Ex: lim (2x+5) / (x+3) = lim (2x+5) / lim (x+3) = (2(2)+5) / (2+3) = 9 / 5
- x->2
-
lim [F(x)]^n = [lim F(x)]^n
- Ex: lim (3x+4)^3 = [lim (3x+4)]^3= [3(1)+4]^3 = 7^3 = 343
- x->1
-
lim n√fx = n√lim F(x)
- Ex: lim √x^2+4 = √lim (x^2+4) = √(2)^2+4 = √8 = 2
-
lim F(x) = F(c)
- Ex: lim (2x-8) = lim F(x) = F(c) = 2(5) - 8 = 2
- x->5
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