Find limit as x approaches two from the left of f of x. and limit as x approaches two from the right of f of x. Someone help??

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Find limit as x approaches two from the left of f of x. and limit as x approaches two from the right of f of x. Someone help??

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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  • phi
Find the limit as x approaches 2 from the left. that means put your finger to the left of 2 (say at x=1) and let x get closer and closer to 2 (but *never* reach it) what is the y value?
0? @phi

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Other answers:

  • phi
what is the y value at x=1?
4?
  • phi
and y stays 4 as you move towards x=2
Ok so would my answers be: As x approaches 2 from the left, the y-value is 4 As x approaches 2 from the right, the y-value is -4 ? @phi
  • phi
yes. The idea (of a limit) is we never let x get to 2, and look at what y is doing as we move *very* close to x=2, y stays 4, and we say the limit is 4 (from the left) and ditto for the right , except y is -4
Oh ok! So should I say the y-value is or the limit is?
  • phi
the limit. the actual y value at x=2 is y= 1 (based on the graph) but the limit is something different.
Oh ok! Thanks so much!
  • phi
you might wonder why we have such a strange idea as limit, but it turns out to be useful.

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