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Nov
14
comment How to find the area inside $x^2+y^2+\sin(4x)+\sin(4y)=4$ using Green's Theorem
There's a thing called "change of coordinates" (in a single integral, this is called "u-substitution"), which by changing the coordinates system (surprise surprise), you can transform the shape to another shape that would be easier to parameterize and integrate. (Though I don't think it works in this case. You can try to change it into something similar to polar coordinates.)
Nov
14
comment How to find the area inside $x^2+y^2+\sin(4x)+\sin(4y)=4$ using Green's Theorem
(The hard part is parameterizing the curve.)
Nov
14
comment How to find the area inside $x^2+y^2+\sin(4x)+\sin(4y)=4$ using Green's Theorem
Green's Theorem is a theorem that relates a double integral to a single integral. To utilize the theorem on finding the area, first set up a double integral of $1$ over the bounded region D. From the theorem you can find that the area is equal to $\oint_{\partial D}x dy$, where $\partial D$ is the positively oriented boundary of the region D.
Nov
14
comment Parameterizing a surface
I see, parameterizations indeed are not unique.
Nov
14
accepted Parameterizing a surface
Nov
14
comment Parameterizing a surface
Wow, thank you for the detailed proof! Took me quite a while to read through it.
Nov
13
revised Parameterizing a surface
fixed small typo
Nov
13
comment Parameterizing a surface
@GitGud The question doesn't explicitly require it to be one-to-one but it might be the reason since this was graded by a computer.
Nov
13
comment Parameterizing a surface
@sanjab - I think this is because we only care about the part that lies in front of the yz-plane.
Nov
13
asked Parameterizing a surface
Nov
2
comment Calculus 7th Ed (Stewart) - Chapter 4 solution 2 page 332
And also it is not *dx. du/dx is not a fraction; you can't just "multiply it to the other side".
Oct
29
comment why there is no derivative in sharp turns?
It's not differentiable because the limits from both sides aren't the same.
Oct
16
revised Turn recursive definition of a function into its close form
edited title
Oct
10
comment Does $2+2$ really equal $4$?
@JimmyK4542 - Here's another one us.metamath.org/mpegif/2p2e4.html
Oct
2
comment Solving with LaGrange multipliers
@Dr.SonnhardGraubner So what you are saying is, by increasing the power by one it would make the equation near impossible to solve?
Oct
2
asked Solving with LaGrange multipliers
Sep
24
awarded  Autobiographer
Sep
21
comment What is the limit of this specific function?
Never thought of this way to solve this problem!
Aug
14
accepted Turn recursive definition of a function into its close form
Aug
14
comment Turn recursive definition of a function into its close form
The problem is that if I were to reuse the computed value of $2^r$ I would have to store it in memory first, which takes more time than just recalculating 1<<r I believe. Nonetheless speed isn't really the most important thing here and as you said, the compiler will optimize it for me at the end anyway. :) Thanks again.