problem sheets to be answered as final exam will have similar questions


problem sheets to be answered as final exam will have similar questions. These would be very good to use for studying we have been told. ( need questions answered in a simplest way possible for me to understand also.) Problem Sheet for Week 1 Question 1: Suppose you have the set of natural numbers N together with the binary operation ? (subtraction). Is the set closed under the operation ? ?

Question 2: Suppose we have integers a,b,c,d (elements of Z) with the properties that a ? b and c ? d. Is it always true that ac ? bd ? Verify the inequality is true provided 0 ? a and 0 ? c

Question 3:Verify that (a2 ?b2) = (a?b)(a + b) (a3 ?b3) = (a?b)(a2 + ab + b2) where a,b ?R

Question 4: Find factorizations for the following values and expressions: 25 91 221 437 439 x2 + x?6 x2 ?5x + 6 x2 + 9

Question 5: Find the solutions to the following equations – assuming they exist. Try factorizing the expressions on the left of the equations x2 ?3x + 2 = 0 2×2 ?x?1 = 0

Question 6: Does the following cubic equation have a real-valued solution? Explain. (Do not try to calculate the solution exactly – just give reasons why you know there must be a solution) x3 ?11×2 + 3x?10

Question 7: Determine if the number 991 is a prime number. If the number is prime at what point can you stop looking for divisors (factors) of the number 991 ? What about in general ? 1

Question 8: Using Euclid’s Algorithm (EA) calculate the greatest common divisor of A = 21 and B = 171. Repeat for A = 221 and B = 247. Repeat for A = 133 and B = 69.

Question 9: A function f(N) is said to be ”order Nk ( written as O(Nk))provided lim?? f(N) Nk ? C for some positive value C and positive value k. Show that f(N) = N3 ?5N2 + 6N ?2 is O(N3) but not O(N2)

Question 10:The exponential function f(x) = ex dominates any ”power of x” function as x increases to in?nity. That is lim xk ex = 0 for every positive value k. Use the power series given below to verify this fact. ex = 1 + x + x2 2! + x3 3! + x4 4! + x5 5! + … its in pdf format…

Order a unique copy of this paper
(550 words)

Approximate price: $22

Basic features
  • Free title page and bibliography
  • Unlimited revisions
  • Plagiarism-free guarantee
  • Money-back guarantee
  • 24/7 support
On-demand options
  • Writer’s samples
  • Part-by-part delivery
  • Overnight delivery
  • Copies of used sources
  • Expert Proofreading
Paper format
  • 275 words per page
  • 12 pt Arial/Times New Roman
  • Double line spacing
  • Any citation style (APA, MLA, Chicago/Turabian, Harvard)

Our guarantees

Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

Money-back guarantee

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

Read more

Zero-plagiarism guarantee

Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

Read more

Free-revision policy

Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.

Read more

Privacy policy

Your email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.

Read more

Fair-cooperation guarantee

By sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.

Read more

Calculate the price of your order

550 words
We'll send you the first draft for approval by September 11, 2018 at 10:52 AM
Total price:
$26
The price is based on these factors:
Academic level
Number of pages
Urgency