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What is the value of lim 4 as x approaches 2?
What is the value of lim 4 as x approaches 2?
What is the value of lim x as x approaches 2?
What is the value of lim x as x approaches 2?
What is the value of lim (2x - 3 + 3x - 5) as x approaches 4?
What is the value of lim (2x - 3 + 3x - 5) as x approaches 4?
What is the value of lim 2x as x approaches 3?
What is the value of lim 2x as x approaches 3?
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What is the value of lim (2x^3 + 3x^2 - 1) as x approaches 4?
What is the value of lim (2x^3 + 3x^2 - 1) as x approaches 4?
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What is the value of lim f(x) as x approaches a if f(x) = c0 + c1x + c2x^2 + ... + cnx^n?
What is the value of lim f(x) as x approaches a if f(x) = c0 + c1x + c2x^2 + ... + cnx^n?
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What is the limit of a polynomial function as x approaches a?
What is the limit of a polynomial function as x approaches a?
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What is the value of lim 3x^7 - 5x^4 + 2x^3 + 9 as x approaches -1?
What is the value of lim 3x^7 - 5x^4 + 2x^3 + 9 as x approaches -1?
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What is the value of lim x^2 as x approaches 2?
What is the value of lim x^2 as x approaches 2?
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What is the value of lim 2x^3 as x approaches 2?
What is the value of lim 2x^3 as x approaches 2?
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Study Notes
Limit Properties
- The limit of a constant is the constant itself:
lim 4 = 4regardless of the value ofx. - The limit of
xasxapproaches a value is the value itself:lim x = 2asx → 2.
Limit Theorems
- The limit of a sum is the sum of the limits:
lim (x + 7) = lim x + lim 7 = 4 + 7 = 11asx → 4. - The limit of a difference is the difference of the limits:
lim (2x - 3 + 3x - 5) = lim 2x - 3 + lim 3x - 5asx → 4. - The limit of a product is the product of the limits:
lim 2x = lim 2 lim x = 2(3) = 6asx → 3. - The limit of a composite function is the limit of the outer function times the limit of the inner function:
lim 2x(3x - 1) = lim 2x lim (3x - 1)asx → 4.
Polynomial Function
- A polynomial function is defined as:
f(x) = c0 + c1x + c2x^2 + … + cnx^n. - The limit of a polynomial function as
xapproachesais:lim f(x) = lim (c0 + c1x + c2x^2 + … + cnx^n) = f(a)asx → a. - To evaluate the limit of a polynomial function, substitute
ainf(x).
Evaluating Limits
- To evaluate a limit, substitute the value of
xinto the function:lim 2x^3 + 3x^2 - 1 = 2(2)^3 + 3(2)^2 - 1 = 27asx → 2. - To evaluate a limit, substitute the value of
xinto the function:lim 3x^7 - 5x^4 + 2x^3 + 9 = -1asx → -1.
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Description
Learn about the properties of limits and how to apply limit theorems to solve problems. This quiz covers the basics of limit theorems and their applications.
