## tjutta Group Title lim x>infinite 1/x^2 S(integral sign) tan^-1 dt one year ago one year ago

1. ash2326 Group Title

$\lim_{x\to \infty} \frac 1 {x^2} \int \tan^{-1} t\ dt$Is this your question?

2. tjutta Group Title

yes sorry Im new to this :-)

3. ash2326 Group Title

No need to be sorry :)

4. ash2326 Group Title

The integral doesn't involve x, so it can be taken out. $\int \tan^{-1} t\ dt\times \lim_{x\to \infty} \frac 1 {x^2}$ tell me what's $\frac 1 \infty=???$

5. ash2326 Group Title

@tjutta ???

6. tjutta Group Title

$\infty$

7. ash2326 Group Title

nope $\frac 1 0= \infty$ so $\frac 1 \infty=???$

8. tjutta Group Title

0

9. ash2326 Group Title

good :D $\int \tan^{-1} t\times 0=???$

10. tjutta Group Title

SIN/COS ? :-)

11. ash2326 Group Title

if you multiply 0 by tan t then what you'd get?

12. tjutta Group Title

0

13. ash2326 Group Title

so it's 0

14. tjutta Group Title

what ? the answer is 0 :-) Ok it makes since if you put it that way but for me whos math retarded its difficult:-)

15. ash2326 Group Title

You know the integral is a variable of t, if you integrate it and multiply by zero. You'd get zero. So it's not necessary to integrate. It's 0

16. ash2326 Group Title

I doubt that this is so easy. I think you have missed some portion of the question. Maybe limits on the integral. Could you check the question again?

17. tjutta Group Title

its just as you put it so I think this is right but I have one more :-) its $\int\limits_{}^{} \frac{ (x^3)\ }{(x-1)^2(x+2) }$ Can you help me with that?

18. ash2326 Group Title

okay, did you try this?

19. tjutta Group Title

I dont know what to do :-) should I start by divide ?

20. ash2326 Group Title

What's the expansion of (x-1)^2?

21. tjutta Group Title

(x-1)(x+1) ?

22. ash2326 Group Title

What would you get if you multiply these?

23. tjutta Group Title

ok I only have 2 ?

24. ash2326 Group Title

$(x-1)\times (x-1)=???$

25. tjutta Group Title

x^2 - 2x + 1

26. ash2326 Group Title

Good:) Numerator we have x^2, so add and subtract (-2x+1) Could you rewrite the integral using this?

27. tjutta Group Title

$\int\limits_{}^{} \frac{ x }{-2x+1 }$ Im I on the right way? I know Im not very good at this at all :-)

28. ash2326 Group Title