- #1
Tekneek
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Why is the limit not just infinity?
wouldn't it be (1-infinity)/(1+infinity)?
wouldn't it be (1-infinity)/(1+infinity)?
Is the Limit as it Approaches 0 Always Infinity?
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In summary, the conversation discusses the concept of limits and specifically addresses the question of why the limit is not always equal to infinity. The conversation also includes an example of a limit problem and how to solve it. The final answer is -7/8.
- #2
mfb
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Why should "-infinity/infinity" be infinity?
What is the limit of
$$\lim_{s \to 0} \frac{\frac{-1}{2}}{\frac{2}{s}}$$?
What is the limit of
$$\lim_{s \to 0} \frac{\frac{-1}{2}}{\frac{2}{s}}$$?
- #3
Tekneek
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mfb said:
-s/4, if s =0 then
Would't the limit be zero?
- #4
mfb
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Sorry typo, this is the formula I meant:
$$\lim_{s \to 0} \frac{\frac{-1}{s}}{\frac{2}{s}}$$
But the more important part was the first question.
$$\lim_{s \to 0} \frac{\frac{-1}{s}}{\frac{2}{s}}$$
But the more important part was the first question.
- #5
Tekneek
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mfb said:
For that formula it would be -1/2. I was thinking it would be infinity because you really can't put down a number with it unless maybe it is 1?
EDIT: Nvm go it. It ends up being -35/40. Thnx
Last edited:
- #6
mfb
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That is not the point. It follows the "-infinity/infinity" type. It is easy to simplify it here to see the limit is not infinity, so your original idea cannot work - that was the purpose of the example.Tekneek said:
I don't understand that question.
Okay.
- #7
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Tekneek said:Why is the limit not just infinity?
wouldn't it be (1-infinity)/(1+infinity)?
Whenever you write "infinity", you should write "a large number".
In this form (1 - a large number)/(1 + another large number) could be any negative number. It could be large and negative or it could be small and negative.
- #8
HallsofIvy
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A very important property of limits, not emphasized enough as I think it should be, is that "If f(x)= g(x) for all x except x= a, then [itex]\lim_{x\to a} f(x)= \lim_{x\to a} g(x)[/itex].
With this particular problem, we can, as long as n is not 0, multiply both numerator and denominator by n. That gives you [tex]\frac{s- 1}{s+ \frac{s+ 4}{7(s+ 5)}}[/tex]. Now, take s= 0.
With this particular problem, we can, as long as n is not 0, multiply both numerator and denominator by n. That gives you [tex]\frac{s- 1}{s+ \frac{s+ 4}{7(s+ 5)}}[/tex]. Now, take s= 0.
- #9
mfb
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You lost two prefactors, HallsofIvy.
$$\frac{s- 1}{s+ \frac{10(2s+ 4)}{7(s+ 5)}}$$
$$\frac{s- 1}{s+ \frac{10(2s+ 4)}{7(s+ 5)}}$$
- #10
HallsofIvy
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Thanks.
- #11
Garrulo
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The limit is of (s-1)/(s+(10*(2s+4)/7(s+5) that doing s=0 result in -7/15
- #12
Mark44
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No, check your algebra. The answer in post #1 (-7/8) is correct.Garrulo said:
1. What is the definition of "limit as it approaches 0"?
The limit as a function approaches 0 is the value that the function approaches as the input (x) gets closer and closer to 0. It is represented by the notation "lim x→0 f(x)" and can be calculated by evaluating the function at values very close to 0.
2. Why is "limit as it approaches 0" an important concept in calculus?
The concept of limit as it approaches 0 is important in calculus because it allows us to understand the behavior of a function near a specific point. It helps us determine if a function is continuous at a certain point and allows us to find the slope of a curve at that point.
3. How do you solve a limit as it approaches 0 algebraically?
To solve a limit as it approaches 0 algebraically, you need to factor the function and simplify it as much as possible. Then, you can substitute 0 for the variable and evaluate the function. If the result is undefined, you can use other techniques such as L'Hôpital's rule or graphing to find the limit.
4. Can the limit as it approaches 0 be a different value on the left and right side?
Yes, the limit as it approaches 0 can be a different value on the left and right side. This is known as a one-sided limit and it means that the function approaches a different value as the input approaches 0 from the left or the right side. If the left and right limits are different, then the overall limit does not exist.
5. How does the concept of "limit as it approaches 0" relate to the concept of continuity?
The concept of limit as it approaches 0 is closely related to the concept of continuity. A function is continuous at a point if the limit as it approaches that point is equal to the value of the function at that point. This means that the function is smooth and has no breaks or sharp turns at that point. Therefore, a function is continuous at a point if and only if the limit as it approaches that point exists and is equal to the function's value at that point.
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