I'm second guessing myself on Limits

  • Thread starter Ithina
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In summary, the conversation is about whether or not the expression (U^2/W^2)^(-1/2) can equal 0. The individual discussing the topic sets the (U/W)^2 part to infinity and shows that the expression becomes 0, but questions if the presence of (i) changes anything. The other person agrees that it is a bit different, but explains that squaring both sides will still result in a limit of 0.
  • #1
Ithina
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Homework Statement



Can [1 - (U^2/W^2)]^(-1/2) equal 0?


Homework Equations


I don't think the other equations are needed.. This is just a tangent of mine from last Physics' lecture.


The Attempt at a Solution



I set the (U/W)^2 part to infinity.
0 = 1 / sqrroot(1 - infinity)

which is:
0 = 1 / infinity*i

I know (1/infinity) goes to 0, but does the (i) change anything other than make it not real? I'm not worried if it's real or imaginary at the moment.
 
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  • #2
you're right it is a bit different however as you see you could always just square both sides which shouldn't make a difference to the limits and you'll still see that it limits to 0 (from the negative)
 
  • #3


As a scientist, it is completely normal to second guess yourself on complex concepts like limits. It shows that you are actively engaging with the material and thinking critically about it. In this case, your attempt at a solution is correct. When (U/W)^2 approaches infinity, the overall expression approaches 0, regardless of the imaginary component (i). This is because as the denominator becomes larger and larger, the overall fraction becomes smaller and smaller, approaching 0. So, yes, the (i) does not change the fact that the expression approaches 0. Keep exploring and questioning, it will lead to a deeper understanding of the concept.
 

What are limits in science?

Limits in science refer to the boundaries or constraints within which a particular phenomenon or variable can occur or be measured. They help scientists understand the range and limitations of their observations or experiments.

Why is it important to consider limits in scientific research?

Considering limits in scientific research is crucial because it allows scientists to accurately interpret their data and draw valid conclusions. It also helps to avoid making false claims or assumptions based on incomplete information.

How are limits determined in scientific experiments?

Limits in scientific experiments are determined through careful planning and design of the study. Scientists must identify all the variables and controls involved and set specific parameters for each one. Data analysis is also used to identify any outliers or anomalies that may indicate a limit.

What are some common factors that can limit scientific research?

Some common factors that can limit scientific research include budget constraints, technological limitations, ethical considerations, and time constraints. In addition, the complexity of certain topics or phenomena may also present challenges in understanding and studying them.

How can scientists overcome limits in their research?

Scientists can overcome limits in their research by collaborating with other experts, using advanced technology, and continuously questioning and refining their methods. They can also seek out alternative approaches or perspectives to gain a more comprehensive understanding of their subject of study.

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