# Precalc

posted by .

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

• ? -

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

• Precalc -

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

• Precalc -

now we are cooking

• Precalc -

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

• Precalc -

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

• Precalc -
• Precalc -

click on "show steps" at upper right of box

• Precalc -

Thanks so much!

• Precalc -

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.

## Similar Questions

1. ### calc

need to find: lim as x -> 0 of 4(e^2x - 1) / (e^x -1) Try splitting the limit for the numerator and denominator lim lim x->0 4(e^2x-1) (4)x->0 (e^2x-1) ______________ = ________________ lim lim x->0 e^X-1 x->0 e^x-1 …
2. ### Calc. Limits

Are these correct? lim x->0 (x)/(sqrt(x^2+4) - 2) I get 4/0= +/- infinity so lim x->0+ = + infinity?
3. ### calc

Are these correct? lim x->0 (x)/(sqrt(x^2+4) - 2) I get 4/0= +/- infinity so lim x->0+ = + infinity?
4. ### Calculus

Show that limit as n approaches infinity of (1+x/n)^n=e^x for any x>0... Should i use the formula e= lim as x->0 (1+x)^(1/x) or e= lim as x->infinity (1+1/n)^n Am i able to substitute in x/n for x?
5. ### Calculus

Show that limit as n approaches infinity of (1+x/n)^n=e^x for any x>0... Should i use the formula e= lim as x->0 (1+x)^(1/x) or e= lim as x->infinity (1+1/n)^n Am i able to substitute in x/n for x?
6. ### Precalc

find the following limit lim n->infinity 2+5n+4n^4/2n show steps please
7. ### college calculus

lim x->a f(x)= 0 , lim x->a g(x)=infinity show that lim x->a [f(x)]^(g(x))= 0
8. ### Calculus

Find the following limits algebraically or explain why they donâ€™t exist. lim x->0 sin5x/2x lim x->0 1-cosx/x lim x->7 |x-7|/x-7 lim x->7 (/x+2)-3/x-7 lim h->0 (2+h)^3-8/h lim t->0 1/t - 1/t^2+t
9. ### MATH

if f(x)=x[x] / sin[x] then show that there is no existence of lim f(x) x>0 2nd prob: show lim (tanx-sinx)/x^3 =1/2 x>0
10. ### Math - Calculus

f(x) = { x^2sin(1/x), if x =/= 0 0, if x=0} a. find lim(x->0)f(x) and show that f(x) is continuous at x=0. b, find f'(0) using the definition of the derivative at x=0: f'(x)=lim(x->0) (f(x)-f(0)/x) c. Show that lim(x->0)f'(x) …

More Similar Questions