The future already exists, you just have to look for it.
Mathematical induction proves statements.
In the past I was taught these steps:
* Show n = 1
* Assume for n = k
* Show n = k + 1
* Then the statement must be true for all n >= 1
But I just memorized them. I was never taught why; I just accepted it as true. We know it can work, of course. But why did we decide one day that this works; and why does it make sense? (Algebraically, geometrically, logically or with calculus?)
( I am not o.k. with just memorizing this. )
This might sound silly, but I’m not sure what to do.
Solve the differential equation
I was like, okay, I need to move the x’s to one side and the y’s to the other side.
Which left me with dy/y^2 =x dx
When you take the integral of each: the dy and dx go away.
Gah, I don’t know.
CITATION ( source) :
Nelsen, R. B. Proofs Without Words: Exercises in Visual Thinking. Washington, DC: Math. Assoc. Amer., 1997.
I did the work, I just want to know if my proof is good enough. The question is shown.
People: Is there any day where you're not doing math homework?
Me : Integrals, integrals, integrals... Rolling around an axis of rotation and creating a solid. Let's calculate the volume. Happy freaking fun time.
[Wake up + Take a shower+ get ready for school + go to school early via bus + work on homework + go to class+ do class activities + class is over + take bus home + do more homework + study + do more homework until you decide to go to sleep ]
I just need help simplifying this to a u not y equation. Any ideas?
Integral of [ y * sqrt(6 + 4y -4y^2) ] dy
Trying to make u = 6 + 4y -4y^2 gives a du= 4 + -4y^2 , and that’s a bit messy.