Question

PLEASE DON'T USE ANY OTHER PROOFS FROM POOFS BY CASES! USE DEFINITION OF ABSOLUTE VALUE! And...

PLEASE DON'T USE ANY OTHER PROOFS FROM POOFS BY CASES! USE DEFINITION OF ABSOLUTE VALUE!

And I was thinking of doing 4 cases:

1. x greater than or equal to  0, and y greater than or equal to  0

2. x greater than or equal to 0, y less than 0

3. x less than 0, y greater than or equal to 0

4. x less than 0 , and y is less than 0.

Proofs by cases - absolute value.

Prove each statement

(d)

For real numbers x and y,  |x+y|≤|x|+|y|.

You can use the fact proven in the previous problem that for any real number z, z≤|z| and −z≤|z|.

Homework Answers

Answer #1

Other way

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Proofs For this assignment, know that: An integer is any countable number. Examples are: -3, 0,...
Proofs For this assignment, know that: An integer is any countable number. Examples are: -3, 0, 5, 1337, etc. A rational number is any number that can be written in the form a/b, a and b are integers in lowest terms, and b cannot equal 0. Examples are 27, 22/7, -3921/2, etc. A real number is any number that is not imaginary or infinity. Examples are 0, 4/3, square root of 2, pi, etc. 1. Prove that the product of...
Exercise 2.5.1: Proofs by cases. Prove each statement. Give some explanation of your answer (b) If...
Exercise 2.5.1: Proofs by cases. Prove each statement. Give some explanation of your answer (b) If x and y are real numbers, then max(x, y) + min(x, y) = x + y. (c) If integers x and y have the same parity, then x + y is even. The parity of a number tells whether the number is odd or even. If x and y have the same parity, they are either both even or both odd. (d) For any...
1a. Using the e − δ definition of continuity, show that the absolute value function f(x)...
1a. Using the e − δ definition of continuity, show that the absolute value function f(x) = |x| is continuous at every point a. 1b. Use the e−δ defintion of continuity to prove that any linear function f(x) = mx+b (with m, b constants) is continuous at every point a. (You should be able to find a formula for δ in terms of e, and the slope m.)
Use strong induction to prove that every natural number n ≥ 2 can be written as...
Use strong induction to prove that every natural number n ≥ 2 can be written as n = 2x + 3y, where x and y are integers greater than or equal to 0. Show the induction step and hypothesis along with any cases
You can't use any constant larger than 8 bits Please don't use codes from other websites...
You can't use any constant larger than 8 bits Please don't use codes from other websites C program Task: * rotateLeft - Rotate x to the left by n bits * Can assume that 0 <= n <= 31 * Examples: rotateLeft(0x87654321,4) = 0x76543218 * Legal ops: ~ & ^ | + << >> ! * Max ops: 25 * Rating: 3 */ int rotateLeft(int x, int n) { return 2; }
Complete a function definition in C for strmatch. For this problem, you can't use any <string.h>...
Complete a function definition in C for strmatch. For this problem, you can't use any <string.h> library functions. In c, two strings match exactly if they have the same characters in the same order and same length. Consider this: int strmatch(const char *x, const char *b); //Needs each of x and y points to the beginning of a string. //Promises to return value 1 if the two strings match exactly. If they don't match, the return value is 0. For...
Use a scatterplot and the linear correlation coefficient r to determine whether there is a correlation...
Use a scatterplot and the linear correlation coefficient r to determine whether there is a correlation between the two variables. Use alphaequals0.05. x 2 4 7 1 6 y 5 8 12 3 11 Click here to view a table of critical values for the correlation coefficient. LOADING... Does the given scatterplot suggest that there is a linear​ correlation? A. ​Yes, because the data does not follow a straight line. B. ​No, because the data follows a straight line. C....
Use the Midpoint Rule for the triple integral to estimate the value of the integral. Divide...
Use the Midpoint Rule for the triple integral to estimate the value of the integral. Divide B into eight sub-boxes of equal size. (Round your answer to three decimal places.)    1 ln(1 + 2x + 5y + z) dV, where B B = (x, y, z) | 0 ≤ x ≤ 4, 0 ≤ y ≤ 8, 0 ≤ z ≤ 4
(i) Use the Intermediate Value Theorem to prove that there is a number c such that...
(i) Use the Intermediate Value Theorem to prove that there is a number c such that 0 < c < 1 and cos (sqrt c) = e^c- 2. (ii) Let f be any continuous function with domain [0; 1] such that 0smaller than and equal to f(x) smaller than and equal to 1 for all x in the domain. Use the Intermediate Value Theorem to explain why there must be a number c in [0; 1] such that f(c) =c
QUESTION 4 In a sample of 110 university lecturers, 96 said that mathematic courses in high...
QUESTION 4 In a sample of 110 university lecturers, 96 said that mathematic courses in high school were the most important source of a student’s success in engineering departments. Test the hypothesis that mathematic courses are the most important sources of a child’s success for at least 79% of university lecturers against the alternative that the population percentage is less than 79%. Use a=0.05. a. Construct hypthesis H0: vs H1: (IMPORTANT: for inequalities use one of the appropriate of the...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT