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plz explain why
[ºs(dr diverges, then the integral ["f(z)dz also d) If f(x) is continuous for...
plz explain why (a) If f(x) is continuous on (a, b), then f(x) +\J(r)l do s...
plz
explain why
(a) If f(x) is continuous on (a, b), then f(x) +\J(r)l do s ſ. 2. \f(x)\dx Answer: True False (b) ST sec(x) tan(x) dx = sec(x)*/3 = sec(7) - sec(1/3) = -1 -2 = -3 #/3 Answer: True False 1 = +00 (c) If an > 0 for all n > 1 and a, converges, then lim 100 Answer: True False
profesor do not accept without explaniation 2. IT/F] Decide if the following statements are true or false. Explai...
profesor do not accept without explaniation
2. IT/F] Decide if the following statements are true or false. Explain (or give a counterexample for) each answer. a) If f(z) is ontinuous and positive forz > 0 and if linn,f(z) = o, then/fe)drconverges. fdz converges. b) The integral / dr diverges c) If bothf(x)d and g(x)da converge, then (().g())dz also converges. d) For any real number p, the integral dz dive
2. IT/F] Decide if the following statements are true or 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...
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...
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)), 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)...
Answer C 6. Let f be a continuous function on [0, oo) such that 0 f(z)...
Answer C
6. Let f be a continuous function on [0, oo) such that 0 f(z) Cl- for some C,e> 0, and let a = fo° f(x) da. (The estimate on f implies the convergence of this integral.) Let fk(x) = kf(ka) a. Show that lim00 fk(x) = 0 for all r > 0 and that the convergence is uniform on [8, oo) for any 6> 0. b. Show that limk00 So ()dz = a. c. Show that lim00 So...
(1) Evaluate the integral (r-1) min(a, y) dy dr, Jo Jo where min(x, y) is the minimum value of r ...
q2 please
(1) Evaluate the integral (r-1) min(a, y) dy dr, Jo Jo where min(x, y) is the minimum value of r and y. (2) Let f,g : R → R be functions of one variable such that f" and g" are continuous. Show that (f"(x)-g"(y)) dydx = f(0) + g(0)-f(2)-9(2) + 2f'(2) + 2g'(0). o Jo (3) Let a > 0. In spherical coordinates, a surface is defined by r = 2acos φ for 0 φ 1. Find the...
Please just explain parts d and f. Part d is 0 and f is true 16....
Please just explain parts d
and f. Part d is 0 and f is true
16. (16 points) Suppose the displacement u(x, t) of a piece of flexible string is given by the initial- boundary value problem t> 0 100uzz = Utt, 0 <3 < 4, u(0,t) = 0, u(4,t) = 0, u(a,0) = 0, u(x,0) = 0(x) +0. (a) (2 points) Give a physical interpretation of Ox). (b) (3 points) In what specific form will the general solution appear?...
plz
explain why
(a) If f(x) is continuous on (a, b), then f(x) +\J(r)l do s ſ. 2. \f(x)\dx Answer: True False (b) ST sec(x) tan(x) dx = sec(x)*/3 = sec(7) - sec(1/3) = -1 -2 = -3 #/3 Answer: True False 1 = +00 (c) If an > 0 for all n > 1 and a, converges, then lim 100 Answer: True False
profesor do not accept without explaniation
2. IT/F] Decide if the following statements are true or false. Explain (or give a counterexample for) each answer. a) If f(z) is ontinuous and positive forz > 0 and if linn,f(z) = o, then/fe)drconverges. fdz converges. b) The integral / dr diverges c) If bothf(x)d and g(x)da converge, then (().g())dz also converges. d) For any real number p, the integral dz dive
2. IT/F] Decide if the following statements are true or 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...
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)...
Answer C
6. Let f be a continuous function on [0, oo) such that 0 f(z) Cl- for some C,e> 0, and let a = fo° f(x) da. (The estimate on f implies the convergence of this integral.) Let fk(x) = kf(ka) a. Show that lim00 fk(x) = 0 for all r > 0 and that the convergence is uniform on [8, oo) for any 6> 0. b. Show that limk00 So ()dz = a. c. Show that lim00 So...
q2 please
(1) Evaluate the integral (r-1) min(a, y) dy dr, Jo Jo where min(x, y) is the minimum value of r and y. (2) Let f,g : R → R be functions of one variable such that f" and g" are continuous. Show that (f"(x)-g"(y)) dydx = f(0) + g(0)-f(2)-9(2) + 2f'(2) + 2g'(0). o Jo (3) Let a > 0. In spherical coordinates, a surface is defined by r = 2acos φ for 0 φ 1. Find the...
Please just explain parts d
and f. Part d is 0 and f is true
16. (16 points) Suppose the displacement u(x, t) of a piece of flexible string is given by the initial- boundary value problem t> 0 100uzz = Utt, 0 <3 < 4, u(0,t) = 0, u(4,t) = 0, u(a,0) = 0, u(x,0) = 0(x) +0. (a) (2 points) Give a physical interpretation of Ox). (b) (3 points) In what specific form will the general solution appear?...
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