True
T(n) =O(S(n)).... Given
T(n) =cS(n)..... Where c is some constant value
S(n) =T(n) /c
S(n) =O(S(n)) /c=O(S(n))
T(n) +2S(n)=O(S(n))+2O(S(n))=3O(S(n))<=O(S(n))
Hence it is true
10 points, 2 points for T/F. 8 points for the justification. 3. Assume you have functions...
11. Circle true or false. No justification is needed. (14 points) (a) If f(x) - o(g(x), and both functions are continuous and positive, then fix dz converges. TRUE FALSE (b) If f(x)- o(g(x)), then f(x)gx)~g(x). TRUE FALSE (c) If the power series Σ an(x + 2)" converges atェ= 5, then it must km0 converge at =-6. TRUE FALSE (d) There exists a power series Σ akz" which converges to f(z)-I on some interval of positive length around FALSE TRUE (e)...
Need help with 1,2,3 thank you.
1. Order of growth (20 points) Order the following functions according to their order of growth from the lowest to the highest. If you think that two functions are of the same order (Le f(n) E Θ(g(n))), put then in the same group. log(n!), n., log log n, logn, n log(n), n2 V, (1)!, 2", n!, 3", 21 2. Asymptotic Notation (20 points) For each pair of functions in the table below, deternme whether...
I need 6(d),7(a) (b) (c) (d). Thank you
in case you can't see the pics.
(a) the NSA 16) (5 ) F o r the RSA SA (d) (5 ) etc) formo CSA) has this w o rth with the RExplain 7. Determine whether each wat is either trofale. If we give justification known fact if Cae, give a comer example (a) (4 points) 2. are vectors of a subpace W of R", then so are all vectors of Span(2.57...
4. Suppose that M C z2 is a non-zero Z-submodule. For each statement below, decide whether i t is TRUE or FALSE and explain your choice. If you use a theorem, clearly state the theorem and why any required hypotheses are satisfied. If you claim a statement is false, provide a counter-example. a. M is a free module. (b) If M happens to be a free Z-module of rank 2, then M -Z2
4. Suppose that M C z2 is...
8) (10 points) Determine if the following are true or false. If false, explain why or give an example to counter the false statement. a) Two events are disjoint if the occurrence of one does not affect the other. b) It is not possible to get a probability of exactly 0. c) Drawing without replacement is an example of dependent events. d) It is possible to have both a disjoint event and an independent event. e) The standard deviation of...
Indicate whether the following statement is true or false) In order to receive full credit, you must provide justification of your answer on the separate sheet you submit(e.g., a proof of a true statement, or a counterexample to a false statement). If f is a continuous function on a smooth curve C' in the xy-plane and Sc f(x, y) ds > 0, then f(x,y) > 0 for all points (x, y) in C. True False
Please answer as quickly u can
Question 5 20 pts Indicate whether the following statement is true or false. In order to receive full credit, you must provide justification of your answer on the separate sheet you submit(e.g., a proof of a true statement, or a counterexample to a false statement). If f is a continuous function on a smooth curve C in the xy-plane and Sc f(x,y) ds > 0, then f(x,y) > 0 for all points (x, y)...
3. (10 pts) For each of the following functions f(n), prove the stated claim by providing constants no C1, and c2 such that for all n2 no, cig(n) S f(n) or f(n) c2g(n), and provide a calculation that shows that this inequality does indeed hold (a) f(n) 2n2 3n3-50nlgn10 0(n3) O(g(n)) (b) f(n)-2n log n + 3n2-10n-10-Ω ( 2)-0(g(n))
Decide whether each statement is true or false and explain your reasoning. Give a counter-example for false statements. The matrices A and B are n x n. a. The equation Ax b must have at least one solution for all b e R". b. IfAx-0 has only the trivial solution, then A is row equivalent to the n x p, identity matrix. c. If A is invertible, then the columns of A-1 are linearly independent. d. If A is invertible,...
complex anaylsis, cite any theorems used, thanks
Z with at (i() Find a single function f(2) which has all of the following: - f(z) is discontinuous at the origin and discontinuous at all points Arg (Z) = t but fczy is continuous all other points of c. f has a simple zero at z=í f has a pole of order 3 at Z=T (ii) Determine whether (*) below is true or false. If true prove it it false, give a...