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)...
FEEDBACK Content attribution QUESTION 10.1 POINT Is the following statement true or false? 00 ch The series about = 0 is an example of a Maclaurin series. n! no Select the correct answer below: O TRUE o FALSE FEEDBACK Content attribution QUESTION 11 . 1 POINT Find the Tadornalinomial for fi R6
5.1 Let U a in f(X;0) ae then E(U)=0. O TRUE O FALSE 5.2 Let X1, ..., X. * N (14.0). If o’ is unknown and we want to derive a confidence interval for the true population mean, then distribution of the appropriate pivotal quantity is Chi-Square with n degrees of freedom. O TRUE O FALSE Q5.3 1 Point 5.3 Let X.....X.1080). Assume both i and o? are unknown. Then the MLE of a' is unbiased, O TRUE O FALSE...
8. If limy/ą. = L where L< 1, then the series Ža, is divergent. True False 10. A power series expansion for f(x) = 0._xj3 is f(x) = {xn-1. True False
please do a,b,c 1. True/False-if true, provide a brief explanation and if false, provide a counterexample. a. Every real valued function has a power series representation about each point in its domain. b. Given a polynomial function f(x) with Taylor series T(x) centered at x a, T(x) = f(x) for all values of a. For a parametrically defined curve, x f(t),y g(t), the second derivative is a'y ("(0-r"C) dx C. Hint: recall the formula from the textbook
True or False: The infinite series 1 +0.1 +0.01 +0.001 +... is divergent True or False: If an diverges, then a, diverges
Question 23 Cultural influences do not affect group communication True False U Question 24 Power in a small group is the ability to influence others. True False Question 25 Infomercials are a great example of a persuasive message O True O False
(a) (1 point) If at converges conditionally, then lak| diverges. Answer: True / False (b) (1 point) Suppose that a power series Eck(-a)* converges for - al > R and defines a function f on that interval. The differentiated or integrated power series converge, provided x belongs to the interior of the interval of convergence. It also claim about the convergence of the differentiated or integrated power series at the endpoints of the interval of convergence. Answer: True / False...
True of False (g) does the power series from ∞ to n=1 (x−2)^n /n(−3)^n has a radius of convergence of 3. (h) If the terms an approach zero as n increases, then the series an converges? (i) If an diverges and bn diverges, then (an + bn) diverges. (j) A power series always converges at at least one point. (l) The series from ∞ to n=1 2^ (−1)^n converges?
(-1) n+1 The series - - +... sums to 3n True False