- #1
applestrudle
- 64
- 0
Homework Statement
lim x->1 (X^9 + x -2)/(x^4 + x -2)
I know how to do this using L'Hopitals Rule and I get 2
Homework Equations
(1+b)^n = 1 + bn + n(n-1)b^2/2! + n(n-1)(n-2)b^3/3! ...
The Attempt at a Solution
Let x = h+1
x -> 1
h -> 0
lim h->0 (h+1)^9 + h-1/(h+1)^4+h-1
lim h->0 h^9 (1+1/h)^9 +h-1/h^4(1+1/h)^4 +h-1
Binomial theorem:
(1+1/h)^9 = 1 +9/h +36/h^2 + 84/h^3 ...
(1+1/h)^4 = 1 +4/h + 6/h^2 + 4/h^3 ...
lim h->0 h^9(1 +9/h +36/h^2 + 84/h^3 ...) +h-1/h^4(1 +4/h + 6/h^2 + 4/h^3 ...) +h-1
This is stil ∞.0 right?
I tried to get rid of the +h-1 at the end by doing
h^7(h^2 +10h +35 +84/h...)/h^2(h^2+5h+5+4/h...)
but then you get ∞.∞