1) Show the absolute value function f(x) = |x| is continuous at every point. 2) Suppose...

1) Show the absolute value function f(x) = |x| is continuous at every point.

2) Suppose A and B are sets then define the cartesian product A * B

Please answer both the questions.

Expert Solution

Colby Messinger answered 2 years ago

Find the absolute maximum value and the absolute minimum value of the function f(x,y) = (1+x^2)(1−y^2)...

Find the absolute maximum value and the absolute minimum value of the function f(x,y) = (1+x^2)(1−y^2) on the disk D = {(x,y) | x2+y2⩽1}?

Suppose a function f : R → R is continuous with f(0) = 1. Show that...

Suppose a function f : R → R is continuous with f(0) = 1. Show that if there is a positive number x0 for which f(x0) = 0, then there is a smallest positive number p for which f(p) = 0. (Hint: Consider the set {x | x > 0, f(x) = 0}.)

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