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[MagmaMcFry]

If you don't care about continuity, the equation exp(x) = c has solutions for all complex c != 0.

[hops]

How do I find the limit in c)? My usual method of equating a_n+1 to a_n gives me a complex number.

It can't possibly just be the lower bound...

[MagmaMcFry]

If you showed b) using the contraction principle, then yeah, the sequence converges to the unique fixed point which you get by equating a_n+1 to a_n, and you made a very simple mistake in the calculation, so try again.

[hops]

Oh, I think I know why it gave me a weird value... I tried dividing both sides by the limit when the limit is zero. I can't believe I actually did something cliche like dividing by zero.

[hops]

I don't really understand the hint...

[hops]

How do I find the maximum value of f(x) = x*cos(x) with x being in [pi,9pi/4)?

[Arx]

Haven't run any numbers, but you can almost certainly just take the point where cos(x) = 1 nearest to the right endpoint, since you know it's going to have larger extrema towards the right.

[MagmaMcFry]

you can almost certainly just take the point where cos(x) = 1 nearest to the right endpoint

The derivative at that point isn't 0, so it isn't even an extreme value.

[hops]

How do I find the general formula of the critical points of xcos(x)?

[MagmaMcFry]

There is none. Either find a solution numerically, or consider that maybe that's not necessary to solve whatever your problem is and you're doing it wrong.

[Parsely]

So the instructor walked through simplifying this problem:
y² - y²x = 1

His first step is:
y²(1 - x) = 1

Bwuh? How did he get "(1-x)" from "- y²x"? _{The rest was intuitive for me to understand.}

[hops]

Here is how I see it, because gathering up common elements look weird sometimes compared to distribution:

y² - y²x = 1

Multiply both sides by y^-2

(y² - y²x)*y^-2 = 1 * y^-2
y^2-2 - y^2-2x = 1 * y^-2
1-x = 1 * y^-2

Multiply both sides by y²

(1-x)*y² = 1 * y^-2+2
y²(1-x) = 1

[hops]

This seem like something simple, but I can't for the life of me figure it out.

What's the nth-derivative of f(x) = ln((1+x)/(1-x))?

[RedWarrior0]

Remember: log a/b = log a - log b.

[hops]

Oh, I kept trying to use the chain rule.