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Anonymous users2024-02-061. Explanation of terms.
Neighborhood: Let sum be two real numbers, and the whole of all real numbers satisfying the inequality is called the neighborhood of the point. The point is called the center of the neighborhood and the radius of the neighborhood.
Absolute value: The distance from a point on the number line to the origin is called the absolute value of , denoted as .
Interval: Let be two real numbers, and , the whole of all real numbers satisfying the inequality is called the open interval and is denoted as . The sum of all real numbers satisfying the inequality is called a closed interval and is denoted as .
where is called the endpoint of the interval. (Changed the main room to an interval, and there was a typographic error in the job).
Number axis: A straight line that specifies the origin point, the positive direction, and the length unit is called the number axis.
Real Numbers: Real numbers are made up of rational numbers and irrational numbers.
2. Fill-in-the-blank questions:
1.The properties of absolute values are
2.The open interval is represented by , which represents the line segment between the point and the point on the number line (excluding the endpoint and ).
3.The representations of the closed interval are , which represent the line segments between the points and points on the number axis (including the endpoints and ).
4. The notation of infinity is:
5, ( denotes all real numbers, or denoted as 6, ( denotes all real numbers satisfying the inequality , or denoted as.
7. ( denotes all real numbers satisfying inequality , or denoted as ;
8. The decentric neighborhood refers to the totality of all real numbers satisfying the inequality and . It is represented by a number line (see the figure of P7, please draw it yourself, it is too troublesome to enter).
9. The number satisfying the inequality -2 1 can be expressed as an interval.
2. Questions and Answers.
1. What should be done in elementary mathematics for advanced mathematics?
Answer: (1) Develop symbolic consciousness and realize the transformation from concrete mathematical operations to abstract symbolic operations. Symbols are a more concise language, borderless, shared by the whole world, and this language has computing power;
2) Cultivate rigorous logical thinking ability to realize the transformation from concrete description to rigorous proof;
3) develop the ability to think abstractly and realize the transition from concrete mathematics to conceptual mathematics;
4) Develop a sense of change and realize the transition from constant mathematics to variable mathematics.
2.What numbers are included in rational numbers?
Answer: Rational numbers include integers and fractions, while integers include positive integers, zeros, and negative integers. Scores in turn include positive and negative scores.
3.Are both two rational numbers on the number line rational between them?
Answer: Not both rational numbers on the number line are rational numbers between them.
4.Which interval is inequality equivalent to 1 x 5?
Answer: Inequality is equivalent to .
5.How is the δ = neighborhood of the point x=1 represented?
Answer:. Some of the content is not displayed on this.
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Anonymous users2024-02-05Belch. There are almost no assessment books available on the Internet, and if it is a single question, someone will answer it for you.
Since you said that it is the first semester of your junior year, then I advise you to focus more on professional courses, because professional courses also have to be studied well, and it is not too late to prepare for the next semester!!
I'd like to ask what the t in the first question is ...... >>>More
The first question is itself a definition of e, and the proof of the limit convergence can be referred to the pee. >>>More
An infinitesimal is a number that is infinitely close to zero, but not zero, for example, n->+, (1, 10) n=zero)1 This is an infinitesimal and you say it is not equal to zero, right, but infinitely close to zero, take any of the values cannot be closer to 0 than it (this is also the definition of the limit in the academic world, than all numbers ( ) are closer to a certain value, then the limit is considered to be this value) The limit of the function is when the function approaches a certain value (such as x0) (at x0). 'Nearby'The value of the function also approaches the so-called existence of an e in the definition of a value, which is taken as x0'Nearby'This geographical location understands the definition of the limit, and it is no problem to understand the infinitesimite, in fact, it is infinitely close to 0, and the infinitesimal plus a number, for example, a is equivalent to a number that is infinitely close to a, but not a, how to understand it, you see, when the chestnut n->+, a+(1, 10) n=a+ is infinitely close to a, so the infinitesimal addition, subtraction, and subtraction are completely fine, and the final problem of learning ideas, higher mathematics, is actually calculus, and the first chapter talks about the limit In fact, it is to pave the way for the back, and the back is the main content, if you don't understand the limit, there is no way to understand the back content, including the unary function, the differential, the integral, the multivariate function, the differential, the integral, the differential, the equation, the series, etc., these seven things, learn the calculus, and get started.
Obviously, physics is simple, and physics is mostly junior high school knowledge, although there are also knowledge involving high school and university, but they are all relatively shallow, so it is quite simple. >>>More