**Find the big−O, big−Ω estimate for x7y3+x5y5+x3y7. [Hint: Big-O, big- Ω, and big-Θ notation can be extended to functions in more than one variable. For example, the statement f(x, y) is O(g(x, y)) means that there exist constants C, k1, and k2 such that |f(x, y)| ≤ C|g(x, y)| whenever x > k1 and y > k2.]**

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big−O:

f(x, y) ≤ Cg(x, y)

f(x, y)=x7y3+x5y5+x3y7 ≤ 3g(x, y)=3x7y7

g(x, y)=3x7y7 , C=2 for $x\ge 1,\ y\ge 1$

big−Ω:

Cg(x, y)≤f(x, y)

3g(x, y)=3x3y3 ≤ f(x, y)=x7y3+x5y5+x3y7

g(x, y)=x3y3 , C=3 for $x\ge 1,\ y\ge 1$