Finding lim f(x) as x->+/- infinity?

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In summary, "lim" stands for "limit," "f(x)" represents a function, and "x->+/- infinity" indicates the direction in which the input is approaching infinity. To find the limit of a function as its input approaches infinity, one can observe the pattern of outputs at larger and larger values of "x." This is important for understanding the long-term behavior of a function and determining if it has a horizontal asymptote.
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mimitka
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Finding lim f(x) as x-->+/- infinity?

f(x)= x^(5/3)-5x^(2/3)

Need to find limit f(x) as x-->+infinity, and x-->-infinity?
 
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Which term dominates as x approaches +/- infinity?
 
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Factor out x5/3: f(x)= x5/3(1- x-1) The limit of 1- x-1, as x goes to plus or minus infinity should be pretty easy. What does that tell you ?
 

Related to Finding lim f(x) as x->+/- infinity?

1. What does "lim" stand for in the phrase "lim f(x) as x->+/- infinity"?

"lim" stands for "limit," which is a mathematical concept that describes the behavior of a function as its input approaches a particular value or direction.

2. What does "f(x)" represent in the phrase "lim f(x) as x->+/- infinity"?

"f(x)" represents a function, where "x" is the input or independent variable, and "f(x)" is the output or dependent variable.

3. What does "x->+/- infinity" mean in the phrase "lim f(x) as x->+/- infinity"?

"x->+/- infinity" represents the direction in which the input "x" is approaching infinity, either from the positive or negative direction.

4. How do you find the limit of a function as its input approaches infinity?

To find the limit of a function as its input approaches infinity, you can evaluate the function at larger and larger values of "x" and observe the pattern of its outputs. If the outputs are approaching a specific value, then that value is the limit of the function as "x" approaches infinity.

5. Why is finding the limit of a function as its input approaches infinity important?

Finding the limit of a function as its input approaches infinity can help us understand the long-term behavior of the function and make predictions about its outputs at extremely large inputs. It also allows us to determine if a function has a horizontal asymptote, which is a line that the function approaches as "x" approaches infinity.

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