Decide if the statement must be true, might be true, or could not be true. The f

Question

Decide if the statement must be true, might be true, or could not be true. The function z = f(x, y) is defined everywhere. If z = e^-(x^4 + y^4), there is a level curve for every value of z. The statement must be true. The statement might be true. The statement could not be true. Decide if the statement below must be true, might be true, or could not be true. The function z = f(x, y) is defined everywhere. If z = e^-(x^10 + y^10), there is a level curve through every point (x, y). The statement must be true. The statement might be true. The statement could not be true.

Explanation / Answer

12. z = e-(x^4 + y^4)

Let c = 2

z = e-(x^4 + y^4) =2

-x4-y4= ln2=0.693

Let c = 0

-x4 -y4= ln(0)

its infinity .

The statement might be true .

13.

z = e-(x^10 + y^10)

There could not be a level curve for every point (x,y)

For example , for value of z = -4 and 4

z = -2 and 2

We found that there is no level curve .

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