I have a question, not pertaining to the posted example...why do we need to account for denominators of 1/x^n when n<1, more than once in the P.F.D.? For example x^3 shows up as A/x + B/x^2 +C/x^3? Unsure as to why?
@MrPaiute To be honest, I'm not completely sure either! The best explanation I've ever gotten is that it's similar to having something like (x+2)(x-1) in the denominator. If you had those two factors, you would have to account for both of them. Well, x^3 is technically three factors, x, x, and x again. You have to account for all three of them. However, if you just do A/x + B/x + C/x, you're decomposition won't work out. So, to distinguish between them, you do x, x^2 and x^3.
I have a question, not pertaining to the posted example...why do we need to account for denominators of 1/x^n when n<1, more than once in the P.F.D.? For example x^3 shows up as A/x + B/x^2 +C/x^3? Unsure as to why?
MrPaiute 4 days ago
@MrPaiute To be honest, I'm not completely sure either! The best explanation I've ever gotten is that it's similar to having something like (x+2)(x-1) in the denominator. If you had those two factors, you would have to account for both of them. Well, x^3 is technically three factors, x, x, and x again. You have to account for all three of them. However, if you just do A/x + B/x + C/x, you're decomposition won't work out. So, to distinguish between them, you do x, x^2 and x^3.
TheIntegralCALC 3 days ago
U are awosome and kind thank u for making this video.
apoorv480 4 weeks ago
@apoorv480 You're welcome! I happy to make the videos. :)
TheIntegralCALC 4 weeks ago