# Precalc

posted by on .

By appropriate calculations, show that:
lim r(x)=5c^4
(x->c)

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I do not think you have given us the whole problem.

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In the problem before it says
r(x)= (x^5 - c^5)/(x-c)
Maybe it's referring to that?
Does that help?

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now we are cooking

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I wish I could say that's why I don't understand this problem. But sadly, I still don't get it. Haha.

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Limit:

Hide steps

lim_(x->c) (x^5-c^5)/(x-c)
Factor the numerator and denominator:
= lim_(x->c) ((c-x) (-c^4-c^3 x-c^2 x^2-c x^3-x^4))
/((c-x) (-1))
Cancel terms, assuming c-x!=0
(c^4+c^3 x+c^2 x^2+c x^3+x^4)
The limit of c^4+c^3 x+c^2 x^2+c x^3+x^4 as x approaches c is 5 c^4

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click on "show steps" at upper right of box

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Thanks so much!

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I just divided the original numerator by (x-c) and got
x^4 + cx^3 +c^2x^2 +c^3 x + c^4
which is 5x^4 or 5c^4 as x-->c

• Precalc - ,

Ah. Alright, I think I understand.