## angela210793 3 years ago Find a and b

1. angela210793

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2. Ishaan94

Hmm $\frac{x^3 + 2x-ax^3+b + ax -bx^2}{x^2-1}$

3. angela210793

then?

4. Ishaan94

Divide it by x^2

5. angela210793

all i know is tht we have fractions like this and limit goes to infinite the limit will b calculated for the monomials in the highest power

6. Ishaan94

x^3 - ax^3 = 0 => a= 1

7. angela210793

where did u get tht???????

8. Ishaan94

$\large \frac{\frac{x^3 + 2x-ax^3+b + ax -bx^2}{x^2}}{\frac{x^2-1}{x^2}} = \frac{x-ax +2\frac1{x} + \frac b{x^2} + \frac {a}{x^2} -b}{1 - \frac{1}{x^2}}$

9. angela210793

Ishaan y u divided it by x^2???

10. Ishaan94

$x\to \infty$ so, if x-ax isn't Zero the limit would approach infinity. And x-ax can be Zero only when a=0.

11. Ishaan94

Hmm it's the matter of choice angela. I felt dividing it with $$x^2$$ would be easier.

12. Ishaan94

Oh sorry, Typo. a=1. not a=0

13. angela210793

ohhh i got it -_- silly me....u did tht so u get lim of those who have x in the denom zero right?

14. Ishaan94

Yes. :-)

15. angela210793

i actually got the same from wht i did

16. vancouver2012

Ishan can you also help me with my pboelm?

17. Ishaan94

Yeah sure. Vancouver

18. angela210793

but...u get infinite lim x->inf(x-ax-b)=0 how did u do it then?

19. Ishaan94

20. vancouver2012

Iright in your left in open questions ;)

21. Ishaan94

$\frac{x-ax +2\frac1{x} + \frac b{x^2} + \frac {a}{x^2} -b}{1 - \frac{1}{x^2}}$With a=1$\large \frac{x-1\cdot x +2\frac1{x} + \frac b{x^2} + \frac {1}{x^2} -b}{1 - \frac{1}{x^2}} = \frac{2\frac1x + \frac{b}{x^2} + \frac1{x^2} -b}{1-\frac1{x^2}}$ $x\to \infty \implies \frac{1}{x}\to 0$ The limit is now $$\frac{-b}1$$.

22. Ishaan94

And a=1, b=0 are the solutions

23. angela210793

@Ishaan Y I no get it ??????

24. angela210793

Ishaan u got a random value of a??? O.o

25. Ishaan94

It's not a random value. $$x-ax$$. and $$x\to \infty$$. It's important form the both terms to cancel out. Which is only possible if a=1.

26. Ishaan94

for* not from

27. angela210793

ohhh.....silly me :S :$:$ got it got it :$:$:$:$

28. angela210793

Thank you Ishaan :D

29. Ishaan94

You're Welcome! :D