So the taylor series for F is just the antiderivative of the taylor series for e^x * 1/sqrt(2pi) with (-x^2) plugged into x

Thanks for the help!

@JC17-OR You're welcome! Here's the full demonstration in case you want it:
F is the antiderivative of f so first find the taylor series of f:
f(x) = (1/sqrt(2pi)) * e^(-x^2)
taylor series for e^y is:
e^y = 1 + y + y^2/2 + y^3/3! + y^4/4! +...
plug in y=-x^2
e^(-x^2) = 1 - x^2 + x^4/2 - x^6/3! + y^8/4! -+...
so f(x) = (1/sqrt(2pi) * (1 - x^2 + x^4/2 - x^6/3! + y^8/4! -+...)
so F(x) = (1/sqrt(2pi)) \* (x - x^3/3 + x^5/10 - x^7/(7\*3!) + x^9/(9\*4!) -+...)

Does anybody have an idea for the power series from the given Taylor series?

@JC17-OR do you mean the radius of convergence?

because the taylor series *is* the power series

Anyway I forgot to mention the radius of convergence is infinity, because f(x) is a probability density function, so the integral of f(x) for x from -infinity to infinity is 1.

I'm dumb that's what I meant to say. I figured it out, thanks for all your help.

@JC17-OR You're welcome!

does anyone know anything about lognormal and weibull distributions?

<@&387091385075105804> ^^^

Need some help with a math problem @here

I have to solve a linear inequality problem:
A delivery driver makes $52 each day that she works and makes approx. $8 in tips for each delivery. If she wants to make $220 in one day at least how many deliveries does she need to make?

Isn't that just 220 = 52 + 8x

Is the $52 a base pay?

If so @Jacob is correct

Is is not (220 - 52) \ 8 = x

Oh jacob beat me to it. Jacob wrote the more proper expression tbh.

Do you solve for x or just leave it as that expression?

Solve for x

You solve for X but he got you started.

Since you get "approximately 8 dollars per tip' the answer will be "about" (whatever x is ) deliveries

Okay that makes sense.

Thanks. Your goy here can't do maths to save himself

Everyone has strengths and weaknesses. This one's pretty basic though. I used Kahn Academy alot in college when I had a foreign teacher who didn't explain things in an articulate manner.

I'm in a learning support math class since my ACT score wasn't high enough to be eligible for me to enroll in the primary math course required for my major.

So I have to take this class and then college algebra class and then hopefully I'm done

Kahn's really good if you prefer to learn with videos

52(base pay) + 8x(tips per delivery >or= to 220

8x >or= 168

x >or= 168/8 = 21 deliveries

At least 21 deliveries in a day

>she
Nice try Schlomo

@Freiheit - CA ?

Making women deliver stuff...sad

220-52=168
168/8=21
21 deliveries

She must live in Texas where tipped pay is $.38/hr or something

Anyone who has taken a class in Differential Equations, could you confirm if the answer in green makes sense?

This section is on series solutions for linear equations

@ButMomShesA300YearOldLoliVampire yes the way you solved it up to the green circle is correct. Now the question asks for you to find two linearly independent solutions. In the green circle you see that after you specify `C_0` and `C_1` that all the other coefficients of a solution are determined. So for one solution choose `C_0 = 1` and `C_1 = 0`, and for the other solution choose `C_0 = 0` and `C_1 = 1`. These solutions are linearly independent since no scalar multiple times the `C_0` and `C_1` of one solution will ever give you the `C_0` and `C_1` of the other solution.

@ThisIsChris Thanks a ton!

@ButMomShesA300YearOldLoliVampire you're welcome!