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(e) lim cr=0 but c.diverges. What is a c, that makes this statement true? 0p
Is the below statement True or False? If lim an=0 then a, must be convergent. n=0
Determine whether each of the following is Always True, Sometimes True, or Always False. If the statement is Always True or Always False, provide a brief justification. If the statement is Sometimes True, provide an example of a series that makes it true and an example of a series that makes it false. In the following, {a_n}∞n=1 is a sequence and {s_n}∞n=1 refers to the corresponding sequence of partial sums. (a) If lim n→∞ s_n = 0, then lim n→∞...
Give a value for "c" and "n0" that makes the following statement true (while c > 0). п(п — 1) 2 (zu)u =
3. Given that lim f(x) = 4 and lim f(x) = -4, what is true about lim f(x)? x-1 4. Given that lim f(x) = 1, lim f(x) = 1, and f(-3) = 1, what is true about lim f(x)? 5. Given that lim f(x) = 0, lim f(x) = 0, and f(2) = 3, what is true about limf(x)? X-3 X-3 X-2
(18. a) Evaluate lim e sin (b) Evaluate lim x sin x 0 x (c) Illustrate parts (a) and (b) by graphing y = x sin(1/x).
(4 pts) Choose the true statement. Let a,b,c e Z with a #0. If a|(b + c) and a|bc, then a|(+ c´). Let a,b,c e Z with a +0. If a|(62 +c), then a|(b+c). Let a, b, ce Z with a + 0. If a|(b+c), then aſb or a|c. Let a,b,c e Z with a +0. If a|(62 +c) and a|(b+c?), then a|(+ c´). the four other possible answers are false
1. Determine whether the statement is true or false. If false, explain why and correct the statement (T/FIf)exists, then lim ()f) o( T / F ) If f is continuous, then lim f(x) = f(r) (TFo)-L, then lim f(x)- lim F(x) "( T / F ) If lim -f(x)s lim. f(x) L, then lim f(x)s 1. "(T/F) lim. In x -oo . (T/F) lim0 ·(T / F ) The derivative f' (a) is the instantaneous rate of change of y...
1. Suppose that lim x) = A, lim f(x) = B, 0) = C, where A, B, C are distinct real numbers. In each of the following, fill in the corresponding box by: • Expressing the limit in terms of A, B, C if it is possible to do so using the given information; • Writing DNE if it is possible to conclude that the limit does not exist using the given information; • Putting a X. otherwise. No explanation...
u(20) for all z e D. Prove tha E C:0<zl<2) and Cr be the positively oriented 9 (10) Suppose that f is analytic in the deleted disk B2(0) C be the positi that If(2)l S M<oo for all z e B2(0). If 0 TS circle |zl r. Show that S 1, then let Cr r | 1= f(z) dz = 0. (Hint: why is the value of (1) the same if C, is replaced by C?
8 10 pts]. For each of the following quantified expressions, find a domain D that makes the statement true, and a domain D that makes the statement false. (a) (Vr E D)y D)[1 < y < 2] (b) (rE D)Vye D)+2y = 3 (c) (rE D)(Vy e D)5y> x (d) (VrE D)Vy E D)(Az E D)[z = +y] (e) (Vr E D)VyED)(AzE D)[z= 8 10 pts]. For each of the following quantified expressions, find a domain D that makes the...