We should think of S as containing all the points OI S anu all puts as limits of convergent sequences of points of S. A slightly different formulation of th notion is given in Exercise 8. an be obtaine EXERCISES 2.2 1. Which of the following subsets of R" is open? closed? neither? Prove your answer. (a) x : 0x < 2} C R (b) {x x 2- for some keN or x= 0} C R (g) : y=xCR : X = y (h) x: 0 x |1}C R" (i) x x 1} C R" j x |x 1} C R" (k) the set of rational numbers, Q CR X (c) C R2 y X (d) y 2 у CR2 1 (1) X: ||X||<1 or X CR2 X (e) : у>х У C R2 (m) (the empty set) X (f) : ху 2 У CR2 2. Let {x} be a sequence of points in R". For i = 1, .. . , n, 1let xi denote the ith coordinate of the vector Xk. Prove that xk a if and only if xk,iai for all i = 1, .. . , n. 3. Suppose {x} is a sequence of points (vectors) in R" converging to a. (a) Prove that |Xk |l a . (Hint: See Exercise 1 17.)

Q: 5. If a number plus 4 equals two times 6, what is the number?

A:

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Q: For problems 5 - 7, evaluate if x = -3 and y = 4. 2x2 - 2xy + 4y

A: Just substitute the given values of x and y in the expression and simplify.

Q: Please do problem 2. Thank you!

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Q: please check my work for this problem. thank you.

A: Yes your work is correct. Well done.

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Q: 8. If you had to use a variable to denote each of the following situations, what could you use? X+…

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Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.