Whether a sentence about high numbers is correct or not

The meaning of the continuous function f(x) at x0 can be understood as follows: when the independent variable x near x0 changes very little, the change of the dependent variable y caused by the function y is also small. That is, in a range around x0, the change in f(x) is also small.

For example, if we make the range around x0 small, then all the values of f(x) in this range will not differ by more than 1 from the values of f(x0).

Thus, because f(x0) is a constant (i.e. a definite number), we can say that in the range around x0 we take, the maximum value of all f(x) will not exceed f(x0)+1 and the minimum value will not be less than f(x0)-1

This means that f(x) is bounded in the range around x0.

The range around x0 can be mathematically denoted as (x0-, x0+)0.

Thus it can be seen that if f(x) is continuous at x0, then there must be >0, so that x belongs to x0- , x0+ ), f(x) is bounded. This statement is true.

This is actually a limit idea, as long as the landlord can think that it can be infinitely small, so close to zero, and because f(x) is continuous at x0 point, then it is naturally impossible for the function value to tend to infinity in such a small range, so that it can be known that there is a boundary.

Correctly, with a continuous definition, there is a δ for arbitrary , such that there is a | in the neighborhood of x0f(x)－a|< i.e. a-

Since whatever elements do not belong to b do not belong to a.

Then we can know that everything that belongs to A must belong to B.

Because we can assume that an element X belongs to A but not to B.

Then because X does not belong to B, according to the title, X does not belong to A, which contradicts the assumption that X belongs to A.

Therefore, it can be concluded that everything that belongs to a must belong to b.

According to the definition of a subset, a is a subset of b.

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Because this sentence can be understood that all elements that belong to a must belong to b, and if a is not a subset of b, then it means that there are elements in the set a that do not belong to b, then these elements that do not belong to b belong to a, which is contrary to the proposition.

For example, at x<0, f(x)=1, at x 0, f(x)=0, and in the interval [-1,1], which is obviously integrable, is the area of the graph. But suppose that the function f(x) has the original function f(x), then the derivative of f(x) should be f(x), which means that f(x) is derivable, but in fact we know that f(x) is not derivable from the fact that the derivative must be continuous.

In fact, the problem is that the two intervals [-1,0) and [0,1] each have their own original functions, but there is no original function as a whole. Do you understand?

I'm sorry I didn't look at the picture carefully, but the examples in the picture are very clear. In example 2, although f(x) has the original function f(x), f(x) has a ** break point when it approaches 0, and there is no way to integrate.

Solution: Because 1 multiplied by any number equals any number Easy to calculate I'm glad to answer for you, I wish you progress in your studies! The Learning Guide team will answer the questions for you.

When x tends to positive infinity, y 2

When x tends to negative infinity, y 2

y ≠ y, so the limit does not exist.