- #1

turdferguson

- 312

- 0

## Homework Statement

Im not good with latex, but Im having trouble with the limit as x approaches -1 of

[sin(x

^{2}+3x+2)]/(x

^{3}+1)

## The Attempt at a Solution

Ive tried substituting u = x

^{2}+3x+2 but I keep getting -1/4 instead of the correct limit 1/3

by long division, x

^{3}+1 = (x

^{2}+3x+2)(x-3) + 7x + 7

This yields the limit as u approaches 0 of

[sin(u)]/[u(x-3) + 7x + 7]

after simplifying sinu/u, I get the limit as u approaches 0 of

1/[x - 3 + (7x+7/u)] = u/[u(x-3) + 7x+7]

If I plug in x=-1, the limit is -1/4, not 1/3. What am I doing wrong?