Question 1. Let x be an integer. Show that if r2 – 4.+ 17 is odd,...
please answer questions #7-13 7. Use a direct proof to show every odd integer is the difference of two squares. [Hint: Find the difference of squares ofk+1 and k where k is a positive integer. Prove or disprove that the products of two irrational numbers is irrational. Use proof by contraposition to show that ifx ty 22 where x and y are real numbers then x 21ory 21 8. 9. 10. Prove that if n is an integer and 3n...
(b) (3 points) Let p(x) = x + x Show that this function is neither odd nor even Then, show that the function defined by h(x) = P(x) - P(-x)] is an odd function 4. (6 points) (a) (2.5 points) Let f(x) = Vä? - 1 and g(x) = (f)(x) and its domain. . Find the product function
1. Prove with a direct proof or disprove by counterexample. If x is an odd integer, then x3 is an odd integer.
Question 9 72 Let In = --* if n is odd and In=1+ if n is even. Vn Find, with proof, lim(sup (In) and lim(inf (In)). If a subsequence En, of the given sequence on, has a limit, L, what can we say about the possible values of L? Explain your answer.
3. Prove, by indirect proof, that if n is an integer and 3n+ 3 is odd, then n is even. Show all your work. (4 marks) MacBook Pro ps lock Command option control option command 20t3 la
Please show all work: Let P1 = 1 If x is odd then Px+1 = 2Px If x is even then Px+1 = 2Px +1 Prove that 2Px+1 + 2Px+1 +1 = Px+2 is true and then solve it.
UUIDOR Quiz 2 - Ma Consider the following theorem. Theorem: The sum of any even integer and any odd integer is odd. Six of the sentences in the following scrambled list can be used to prove the theorem. By definition of even and odd, there are integers rands such that m = 2r and n = 2s + 1. By substitution and algebra, m + n = 2r + 25 + 1) = 2(r + s) + 1. Suppose m...
4.(15 pts) Let a be a positive odd integer. Find the value of the following integral in terms of a using substitution with u = = sin(ax). jë sinº (ax)cosº (ax) dx 5. (10 pts) Let a, b, and cbe positive integers. Evaluate the following limit. If you use 2 Hospital's Rule, be sure to give indeterminare pe and mention when you inoke it. In (a+beck lim 06 x
Please show all work: Let If x is odd then If x is even then Prove that is true and then solve it. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Let P1 = 1 If x is odd then Px+1 = 2Px If x is even then Px+1 = 2Px +1 Show this is true and solve it: 2Px+1 + 2Px+1 +1 = Px+2