plz explain why (a) If f(x) is continuous on (a, b), then f(x) +\J(r)l do s...
Problem 13 (9 point) Circle your answer for the following statement (True or False). If it is true, explain why. If it is false, explain why or give an example that disproves the statement. To get a mark, you need to give an explanatio. (a) If f(t) is continuous on (a,b], then f(x) + f(t) -dx < 2 Answer: True False 1 sca) de (b) [sec(z) tan(x) dx = sec(x)ys = sec(7) – sec(7/3) = -1- 2 = -3 Answer:...
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...
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
any help would be awesome Explain why or why not Determine whether the following state- ments are true and give an explanation or counterexample. a. The sum Σ is a p-series. b. The sumeve IS a p-series. c. Suppose f is a continuous, positive, decreasing function, for re l'and ak =f(k), for k = 1,2,3, . . . . If Σ@g converges to L, then | f(x) dx converges to L. d. Every partial sums, of the series Σ underestimates...
Let f : [a, b] → R and xo e (a,b). Assume that f is continuous on [a,b] \{x0} and lim x approaches too x0 f(x) = L (L is finite) exists. Show that f is Riemann integrable. 1. (20 pts) Let f : [a, b] R and to € (a,b). Assume that f is continuous on [a, b]\{ro} and limz-ro f (x) = L (L is finite) exists. Show that f is Riemann integrable. Hint: We split it into...
Help on number 2 A-C Math 166 Spring 2020 Lab 12 - Integration Strategies and Improper Integrals 1. Evaluate the following integrals. (a) | In(x2 + 2a) dx 100 dx (8) Jo Je to (1) ["* sin(a) Vsee(2) de 5 1 11 x² – 2x – 3 dx 87/2 13 x(lnx)2 de (c) / tarda (1) [4x*e*** de 2. For what values of p do the following improper integrals converge? (1/2 da (0) Le 2 In () Jo 3. Give...
3) Prove that there exists f : R → R non-negative and continuous such that f € L'OR : dm) ( i.e. SR \f|dm <00) and lim sup f(x) = ∞. 2-0
Please give clear detailed explanation. Let a 0 and suppose that the function f is Riemann integrable on [0, a]. Prove that f(a-x) dx = 2S0[f(x) + f(a- 1 ca f(x) dx = x)j dx. Prove that f' in(1 + tan(a) tan(x)) dx = a ln(sec(a)) (0<a<T/2) Let f: [0, 1] → R be defined by f(x) = VX , 0 1 , and let x 2 n-1,2 be a partition of [0, 1]. Calculate lRll and show that lim...
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)...
3. Suppose f : [0,) + R is a continuous function and that L limf(x) exists is a real number). Prove that f is uniformly continuous on (0,.). Suggestion: Let e > 0. Write out what the condition L = lim,+ f(t) means for this e: there erists M > 0 such that... Also write out what you are trying to prove about this e in this problem. Note that f is uniformly continuous on (0.M +1] because this is...