UNSW 2024 Finals #2

Some practice problems for YOU:
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[@idontknow-wl6su]

Tricky, i have to learn a lot for seeing those things D':, btw, thanks for share interesting problems :D

[@owlsschoolofmath9732]

Thanks! Glad you like it. I do find that it helps so much just seeing and doing a lot of problems. 👍👍

[@Namo_Amitabha2024]

I’m used to u=x+1/x, so I divide top and bottom by x^2, and factor the numerator. This gives us u/(u^2-2)du, which yields the same result. Another line of thought is to keep dividing by x until top looks like derivative of the bottom, which leads to your solution. Interesting.

[@owlsschoolofmath9732]

Nice! Yes that keep dividing method sounds pretty good too. Quite a few good ways on this one. 👍

[@abhinav2584]

Isnt d(x^-2)/dx = -2*1/x

[@owlsschoolofmath9732]

Hello. No, by power rule decrease power by one and you have -2/x^3. Make sense?