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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.
t=w,w 2 L.H.S (w+w 2 ) + (w 2 + w) 2 ........ 1 + 1 ..... But every third term is of the form: (w 3n +w 3n ) 2 =22 There are nine such terms. Their sum is 36. The rema
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Change of base: The final topic that we have to look at in this section is the change of base formula for logarithms. The change of base formula is,
Two sessions of swimming lessons were held at a pool. In the first session 40 students attended. Of these 40 students 60% were girls. How many girls attended the first session of s
NUMBER SYSTEMS: Numbers are intellectual witnesses that belong only to mankind. Example: If the H C F of 657 and 963 is expressible in the form of 657x + 963 x -
A man invests rs.10400 in 6%shares at rs.104 and rs.11440 in 10.4% shares at rs.143.How much income would he get in all?
Negative four is multiplied through the quantity x + 8. If 6x is then added to this, the output is 2x + 32. What is the value of x? twice the quantity x + 6 is divided by negative
how to make a tape diagram and a equivalent ratio
A boy covered half of distance at 20km/hr and rest at 40kmlhr. calculate his average speed.
2x^3+5x^2+2x+5
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