- #1
What Are the Properties of Limits in Mathematics?
- Thread starter nycmathguy
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Homework Help Overview
The discussion revolves around the properties of limits in mathematics, specifically focusing on a limit involving the cube root function and its behavior around a particular point. Participants explore the implications of modifying a function at a specific point and how it affects the limit.
Discussion Character
- Conceptual clarification, Assumption checking, Mixed
Approaches and Questions Raised
- Participants question the reasoning behind taking the cube root and then cubing the result. There is exploration of how changing the function at a specific point impacts the limit, with some participants suggesting that the limit remains unchanged despite the modification.
Discussion Status
There is an ongoing exploration of the concept of limits, particularly in relation to continuity and discontinuity. Some participants have provided insights into the nature of limits and how they are determined by the behavior of functions around points of interest, while others express confusion about the context of limits in precalculus.
Contextual Notes
Participants note a potential confusion regarding the placement of limits in precalculus materials and question the appropriateness of their inclusion in that context.
- #2
Doc Al
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You took the cube root of 8 (81/3) and then cubed it. Why?
- #3
nycmathguy
Let's take it from here:Doc Al said:
(1/4)[cr{8}]
(1/4)(2)
1/2
The limit is 1/2.
Why cubed the cube root of 8 in my first attempt?
Answer: typo
- #4
Doc Al
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OK, now you've got it.
- #5
Delta2
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Yes the limit is 1/2. If we tweak the function and we make it so that f(x) is the same as before for all ##x\neq 8## but we set ##f(8)=256## what will the limit be?
- #6
nycmathguy
The limit would be 256.Delta2 said:
- #7
Delta2
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Nope it will remain 1/2. For the limit we focus what happens around the point of interest but not necessarily onto the point of interest. Around 8 the tweaked function remains the same so the limit remains the same. I just introduced an artificial discontinuity in the tweaked function by setting f(8)=whatever except 1/2.nycmathguy said:
I guess you need to be introduced to continuity and discontinuity by your textbook. If it is not done by your precalculus book, it should be done by your calculus I book.
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What are limits doing in a pre-calculus book, one wonders?Delta2 said:
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Delta2
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The boundaries between calculus and precalculus are fuzzy, at least that's what Ron Larson thinks lol...PeroK said:
- #10
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