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1. The problem statement, all variables and given/known data

i am terrible with latex, so i will just write it down.

integ of 1/(x^3+x^2+1)dx

and the limit i am trying to do it without using the l'hopital rule. By the way i also would like to know if there exists any theorem which states that, if the limit of a functions can be calculated using l'hopital rule, than it will be solvable also without using l'hopital rule??

lim{x-->0)(x cos(x)-sin(x) )/( x- sin(x) )

using l'hopital rule, the limit is -2

thnx in advance

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Integral, and limit help?

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