profesor do not accept without explaniation 2. IT/F] Decide if the following statements are true or false. Explai...
1. Decide if the following statements are true or false. Give an explanation for your answer. (a) If 0 < an < bn and Σ an converges, then Σ bn converges (b) If 0 < an < bn and Σ an diverges, then Σ bn diverges. (c) If bn an 0 andbcoverges, then an converges (d) If Σ an converges, then Σ|an| converges (e) If Σ an converges, then linn lan +1/a (f) Σχ00(-1)"cos(nn) is an alternating series (g) The...
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)...
Detailed proof please. . 1. Determine whether the following statements are true or false. If one is true, provide a proof. If one is false, provide a counterexample (proving that it is in fact a counterexample). IF f is a positive continuous function on [1,00) and (f(x))2dx converges, THEN Sº f(x)dx converges. • IF f is a positive continuous function on [1,00) such that limx700 f(x) O and soon f(x)dx converges, THEN S ° (f (x))2dx converges. IF f is...
Please only answer questions a, d, and f. Thank you. 1. True/False Explain. If true, provide a brief explanation and if false, provide a counterexample. Choose 3 to answer, if more than 3 are completed I will pick the most convenient 3. Given a sequence {an} with linn→alanF1, it follows that linnn→aA,-1. b. A series whose terms converge to 0 always converges. c. A sequence an converges if for some M< oo, an 2 M and an+1 >an for all...
1. State whether the following statements are true or false. Give reasons for your answer (a) If limko WR=0 then our converges (b) = 5 means that the partial sums converge to 5 (c) E U is called conditionally convergent if it satisfies the conditions of the alternating series test (d) The limit comparison test applies only to series which are positive from some point on (e) (-2)* = 5 (f) If uk = (2k + 1)! then uk+1 =...
Determine whether the statement is true or false. If false, explain why or give a counterexample that shows it is false. (2 pts each) b. If f(x,y) S g(x, y) for all (x, y) in , and both f and g are continuous over 2, then c. If f is continuous over 2 and 22, and if JJ, dA- jJa,dA, then f(x.y) dA- Jf(x.y) dA for any function fx,y). Determine whether the statement is true or false. If false, explain...
plz explain why [ºs(dr diverges, then the integral ["f(z)dz also d) If f(x) is continuous for all x and diverges for any a > 0. Answer: True False 0.8P(1 -0.001P). Then lim P(t) = 800. dP (e) Consider the logistic model dt Answer: True False (f) Let fa. denote the average value of over the interval (a, b). Then - Blac) + Sic for all ce(a,b). Answer: True False
4. True or False. Label each of the following statements as true or false. If true, give a proof, if false, give a counterexample. (a) Every nontrivial subgroup of Q* contains some positive and some negative numbers (b) Let G be a finite group. Let a E G. If o(a) 5, then o(a1) 5. (c) Let G be a group and H a normal subgroup of G. If G is cyclic, then G/H is also cyclic. (d) Le t R...
if false, plz do give a data set, thanks 2. Decide if the following is true or false: In every RBD setup, either the MSTR MSE or MSB2 MSE (or maybe both). If it is true, explain why. If it is false, give a data set that is a counterexample. 2. Decide if the following is true or false: In every RBD setup, either the MSTR MSE or MSB2 MSE (or maybe both). If it is true, explain why. If...
can you solve for me the exercises 2 in class I need all of these please thank you so much Exercise 10. Show that J dz converges. Class Exercise 2. Use integration, the direct comparison test, or the limit comparison test to determine whether the integral converges or diverges. tan 6 de x/2 (a) a (b) 2re- (e) fo (d) (e) Jo (f) (s) dr dt vt+sint dr +1 da 1-2 1 de 1+e dr Foo 2+cosz dr (h) ()...