The Weierstrass theorem (1) draw diagram of cases in which a feasible set (budget set) is not closed or not bunded,but a solution to the optimization problem exists. (in the case of drawing a graph, one of the feasible sets (budget set) is not closed or bunded, but there is a solution to the optimization problem.) (2)show f(x)=1,g(x)=x are continuous functions. It is shown that f (x) = 1, G (x) = x are continuous functions (3)Does the following function has a maximum on the inverval [-1,1]?If not,explan why. Does the following function have a maximum interval [- 1,1]? If not, please explain the reason f(x)= 1/x,x=/=0； 0,x=0.

The Weierstrass theorem (1) draw diagram of cases in which a feasible set (budget set) is not closed or not bunded,but a solution to the optimization problem exists. (in the case of drawing a graph, one of the feasible sets (budget set) is not closed or bunded, but there is a solution to the optimization problem.) (2)show f(x)=1,g(x)=x are continuous functions. It is shown that f (x) = 1, G (x) = x are continuous functions (3)Does the following function has a maximum on the inverval [-1,1]?If not,explan why. Does the following function have a maximum interval [- 1,1]? If not, please explain the reason f(x)= 1/x,x=/=0； 0,x=0.

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What is the content of stone – Weierstrass theorem? In which course do you learn it?

If x is a compact Hausdorff space, a is a subalgebra of C (x, R) (a real valued function on x), and a contains non-zero constant functions, then a is dense in C (x, R) if and only if a can distinguish points (that is, any XY, there exists a function f, f (x) f (y) in a)

On the problem of non mutation of spring
A light spring is placed vertically, one end is fixed on a horizontal plane, and the other end is connected with a mass m block. Now a vertical pressure f is used to keep the block at rest. When f is removed suddenly, the acceleration of the block is f / m. (but why can't it be zero, and the spring can't change suddenly?) (if the spring is cut short without removing F, how will it change?)

When the object is in a static state, the resultant force of gravity, F and elastic force is zero. [when f is suddenly removed, the elastic force of the spring has no time to change], then the resultant force of gravity and elastic force is equal to F. according to Newton's second law, the acceleration of the object is a = f / m at the moment when f is suddenly removed
If the spring is cut short without removing F, it should be: a = [F + Mg] / m