f(x)=x^4+2x+1
lim x goes to 1 (f(x)-4x)/(x^3-1)=?

Question

f(x)=x^4+2x+1 
lim x goes to 1 (f(x)-4x)/(x^3-1)=?

amistre64 · Answer

replace f(x) with it "value" into the 2nd equation....

x^4 +2x +1 -4x // x^3 -1

amistre64 · Answer

the top and bottom differ by 1 degree so you asymptote with be a slant or oblique  at y=x

amistre64 · Answer

i saw the words corectly in my head, but my fingers are forming a coop....

anonymous · Answer

I still can't find solution prof. :/

anonymous · Answer

I know, i should simplify equation and plug in 1.But can't simplify.

anonymous · Answer

You can't place 1 for x into the equation as you might with other problems because in $$f(x)= (x^4-2x+1)/(x^3-1)$$ placing 1 in for x would result in a zero in the denominator. You have to first get rid of the x^3-1 in the denominator

anonymous · Answer

I know , but i can't get rid of the x^3-1 denominator, i have tried to simplify but couldn't.Can you show how ?

amistre64 · Answer

i thought it said as x _. infinty...im going blind i tellya ....BLIND!!

amistre64 · Answer

x->....and my hand eye brain coordination is getting shot....

amistre64 · Answer

x^3 - 1 is a difference of cubes right?

x^3 - 1^3

amistre64 · Answer

(x-1)(x^2 +x +1) is its factor

anonymous · Answer

Yeah ,it equals  (x-1)(x^2+x+1)

amistre64 · Answer

facotr the top and see if x-1 cancles

anonymous · Answer

You need to simplify using the differnce of cubes:
$$f(x)= (x^4-2x+1)/((x-1)(x^2+x+1))$$
You c\]an then use long division on the numerator (divide the whole top by x-1 to get
[f(x)= (x^3-x^2+x-1)/(x^2+x+1)\

amistre64 · Answer

yeah that way....lol

anonymous · Answer

The bottom part glitched up but you get the point.

anonymous · Answer

Cheers! I got it ツ

amistre64 · Answer

I get:

(x-1)(x^3 +x^2+x -1)

anonymous · Answer

Yeah (x-1)(x^3 +x^2+x -1)

amistre64 · Answer

2/3 as the limit?  as x->1 ?

anonymous · Answer

X^2 would have to be negative because you're dividing by (x-1). Once you multiply (x-1) by x^3 to get rid of the x^4, you would get -x^3

anonymous · Answer

Yep 2/3,

amistre64 · Answer

it aint negative....i double checked that ;)

anonymous · Answer

I made Polynomial long division and it's positive , but thanks Athenian

amistre64 · Answer

1 | 1 0  0  -2   1
     0  1  1   1 -1
    -------------
      1  1 1  -1  0

x^3 +x^2 +x -1

amistre64 · Answer

yeah, good job Athen....really, that was great work :)