Posted by Grace on .
By appropriate calculations, show that:
lim r(x)=5c^4
(x>c)

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

Precalc 
Grace,
In the problem before it says
r(x)= (x^5  c^5)/(xc)
Maybe it's referring to that?
Does that help? 
Precalc 
Damon,
now we are cooking

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

Precalc 
Damon,
Limit:
Hide steps
lim_(x>c) (x^5c^5)/(xc)
Factor the numerator and denominator:
= lim_(x>c) ((cx) (c^4c^3 xc^2 x^2c x^3x^4))
/((cx) (1))
Cancel terms, assuming cx!=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 
Precalc 
Damon,
I got that from
http://www.wolframalpha.com/input/?i=limit+%28x^5++c^5%29%2F%28xc%29++as+x%3Ec 
Precalc 
Damon,
click on "show steps" at upper right of box

Precalc 
Grace,
Thanks so much!

Precalc 
Damon,
I just divided the original numerator by (xc) 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 
Grace,
Ah. Alright, I think I understand.