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Level Curves or Contour Curves
Another topic that we should look at is that of level curves or also known as contour curves. The level curves of the function z = f (x, y) are two dimensional curves we acquire by setting z = k , where k is any number. Thus the equations of the level curves are f (x, y) = k .
Notice: occasionally the equation will be in the form f (x, y, z) = 0 and in these cases the equations of the level curves are f (x, y, k) = 0.
You have probably seen level curves (or contour curves, doesn't matter whatever you want to call them) before. If you have ever observed the elevation map for a piece of land, this is not anything more than the contour curves for the function that provides the elevation of the land in that area. Actually, we probably do not have the function which gives the elevation, although we can at least graph the contour curves.
sum of zero of polynomial x2-2x+1is equal to sum of zero of polynomial x3-2x+x then find the product of all the three zero of the second polynomial
2yx+3y=30
show that one of the straight lines given by ax2+2hxy+by2=o bisect an angle between the co ordinate axes, if (a+b)2=4h2
Carl worked three more than twice as many hours as Cindy did. What is the maximum amount of hours Cindy worked if together they worked 48 hours at most? Let x = the amount of h
jack and his mother paid $11.50 for tickets to the movies. An adult''s ticket costs $4.50 more than a child''s ticket. What was the cost of each ticket?
Find out the length of y = ln(sec x ) between 0 x π/4. Solution In this example we'll need to use the first ds as the function is in the form y = f (x). So, let us g
Functional and variations.Block III, Consider the functional S[y]=?_1^2 v(x^2+y'')dx , y(1)=0,y(2)=B Show that if ?=S[y+eg]-S[y], then to second order in e, ?=1/2 e?_1^2¦?g^'
How many integers satisfy (sqrt n- sqrt 8836)^2 Solution) sqrt 8836 = 94 , let sqrt n=x the equation becomes... (x-94)^2 (x-94)^2 - 1 (x-95)(x-93) hence 93 8649 the number o
Rule 1 The logarithm of 1 to any base is 0. Proof We know that any number raised to zero equals 1. That is, a 0 = 1, where "a" takes any value. Therefore, the loga
Difference between absolute and relative in the definition Now, let's talk a little bit regarding the subtle difference among the absolute & relative in the definition above.
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