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anonymous
 4 years ago
what are level curves? please explain in easy way..
anonymous
 4 years ago
what are level curves? please explain in easy way..

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JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.0Level curves are explained at the beginning of this lecture: http://ocw.mit.edu/courses/mathematics/1802multivariablecalculusfall2007/videolectures/lecture8partialderivatives/

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0f(x,y)=c is a level curve what do you think about f(x,y)=z and f(x,y,z)=0 are these also level curves? if so then please tell the reason if you can. also tell me that in level curves the space between one level curve to another must be same?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0what's the difference between level curves and level surfaces?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i have listened the lecturere and found it very helpful but i want to clearify above points. please explain if u can...

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.0z = f(x,y) is a way to graph the function f(x,y) in the 3dim space. In 3d space, z = f(x,y) describes a surface. The level curves in this case are values where f(x,y) = c, a constant. Equivalently, it's when z = c, because z = f(x,y). If f(x,y) = 0, that will describe the level curve for when the function is zero. Equivalently, it describes the level curve for when z = 0 where z = f(x,y). f(x,y,z) is a function of three variables. ideally, we would graph it in 4d space. But we have a very hard time imagine 4d space. For that reason, we consider the equivalent of level curves for this function: f(x,y,z) = c. But now, instead of describing curves in 2d space as do level curves of the form f(x,y) = c, the equation f(x,y,z) = c describes a surface. For example, if the function where \[ f(x,y,z) = x^2 + y^2 + z^2 \] then f(x,y,z) = c, where c > 0, describes a sphere.
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