Question

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

Answer 1

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

Answer 2

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

Answer 3

now we are cooking

Answer 4

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

Answer 5

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

Answer 6

I got that from
http://www.wolframalpha.com/input/?i=limit+%28x^5+-+c^5%29%2F%28x-c%29++as+x-%3Ec

Answer 7

click on "show steps" at upper right of box

Answer 8

Thanks so much!

Answer 9

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

Answer 10

Ah. Alright, I think I understand.