Can Taylor Series Help Solve This Integral and Limit?

[sutupidmath]

integral, and limit help?

well i have this integral, i have tried to solve it but got nowhere.
it is:

\int\frac{\1{x^3+x^2+1}

and the limit is

 

[EnumaElish]

You should post this under the applicable homework help section.

 

[sutupidmath]

i am terrible with latex, so i will just write it down. Btw it is not a homework.

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) )

thnx in advance

 

[sutupidmath]

well, no ideas on how to tackle those two problems so far?

 

[EnumaElish]

Even if it's not "officially" homework, for this type of a problem you have a better chance of getting a response in the applicable HW section.

 

[ice109]

what is the limit? you didn't write it down? and the integral using partial fractions i think

 

[sutupidmath]

what is the limit? you didn't write it down? and the integral using partial fractions i think

well, i wrote the limit down, read post #3.
About the integral i also think that somewhere along the way i have to use partial fractions, but how to go about factoring the denominator.??

 

[TheoMcCloskey]

Regarding the limit, you could expand the trig terms in Taylor series and collect terms. You should find that you'll be able to divide numerator and denominator by a factor of x^3 to obtain a leading term that is your limit as x approaches zero.

Of course, confirm your answer with L'hopital (requires three applications)