MHB Integration by parts, Partial fraction expansion, Improper Integrals

[ertagon2]

View attachment 7785

1. -
2. check if right
3. check if right
4. Now, 2 seems to be the right answer for A yet when i made x=5 and subtracted new form form the old one I got a difference of ~$\frac{4}{9}$ (should be 0 obviously) I got A=2 B=$\frac{45}{21}$ C=2
5. How to calculate $\lim_{{x}\to{\infty}}(- e^{-x})$

 

[Dethrone]

2. Correct
3. Yes, notice that it's an odd function $f(-x)=-f(x)$ so the "areas" cancel out.
4. Might want to check your math here a bit. The answer is correct ($A=2$), but $B=3$ and $C=-2$.
Also, $\lim_{{x}\to{\infty}}(e^{-x})=\lim_{{x}\to{\infty}}1/e^x=0$ since the denominator goes to infinity.

 

[Prove It]

Since when is 0.25 a fraction in simplest form?

 

[ertagon2]

Since when is 0.25 a fraction in simplest form?

so =$\frac{1}{4}$ ?