QUESTION 5 2x Given that f(x)= is continuous and decreasing on [3,+). x2 +4 Determine the...
We have the following Limit Comparison Test for improper integrals: Theorem. Suppose f(x), g(x) are two positive, decreasing functions on all x > 1, and that lim f(x) =c70 x+oo g(x) Then, roo 5° f(x) dx < oo if and only if ſº g(x) dx < 00 J1 (a) Using appropriate convergence tests for series, prove the Limit Comparison Test for improper integrals. (Hint: Define two sequences an = f(n), bn = g(n). What can you say about the limit...
I would really appreciate your help with solving this whole question of my assignment due in a few hours. Willing to rate and like!! Thank you so much Q1/ Solve the following series question a) is the following sequence increasing, decreasing, or not monotonic? Is the sequence bounded? a. an = 2n13 b) Use power series to approximate the definite integral to six decimal places. a. Jo 773 dx b. So 2 x ln(1 + x²) dx 0.3 x c)...
Find the Taylor polynomial of order 3 centered at 0. f(x) = com 6-X pg(x) = - * x4 x2 36 + + x3 216 x2 216 + х 36 + + P3(x) = 5 P3(x) = 1296 x3 1296 x4 1296 x2 + 6 36 x3 216 x2 216 P3(x) = х 1 6 + x3 1296 36 Find the quadratic approximation of fat x = 0. f(x) = sin In(2x + 1) P2(x) = 2x + 2x2 p2(x)...
QUESTION 4 Given f(x)=2x-5 and g(x)= x2 + x - 20, find each: a) [fog)(3) b)[gºf](x) IT I Arial 3(12pt » T.:= . 31.25
(2x - 1 if x < -1 2. Suppose f(x) = 2x2 - 4 if-1<x52 (log: (x - 1) if x > 2 a) Is f continuous at x = -1? Justify your answer completely. b) Is f continuous at x = 22 Justify your answer completely. 3. Suppose f(x) = x2 + 3x a) Using the definition of derivative, find f'(x). No credit will be given if shortcuts are used. b) Find the equation of the tangent line to...
Let f be a positive, continuous, and decreasing function for x ≥ 1, such that an = f(n). If the series ∞ an n = 1 converges to S, then the remainder RN = S − SN is bounded by 0 ≤ RN ≤ ∞ N f(x) dx. Use the result above to approximate the sum of the convergent series using the indicated number of terms. (Round your answers to four decimal places.) ∞ n = 1 1 n2 +...
point) Consider a function f(x) that has a Taylor Series centred at x = 5 given by ſan(x – 5)" n=0 he radius of convergence for this Taylor series is R= 4, then what can we say about the radius of convergence of the Power Series an ( 5)"? nons A. R= 20 B.R= 8 C. R=4 D. R= E. R= 2 F. It is impossible to know what R is given this information. point) Consider the function f(x) =...
Let f be a positive, continuous, and decreasing function for x 2 1, such that a, = f(n). Note that if the series, converges to S, then the remainder R - S - Sis bounded by OSRNS / (x) dx. Use these results to find the smallest N such that RN 30.001 for the convergent series.
22 . . 23 . 24 Use the binomial series to expand the function as a power series. 7 (4 + x) 3 Σ Your answer cannot be understood or graded. More Information n = 0 X State the radius of convergence, R. R = 4 Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. f(x) = x cos(4x) D) n = 0 Evaluate the indefinite integral as an infinite series. I conte...
Find the power series representation for 2x-4 x2-4x + 3 What is its interval and radius of convergence? Find the Maclaurin series for f(x) (1 z)2 What is its radius of convergence? Find the Taylor Series for f(x) AC Centred at a =-3. What is its radius of convergence? Find the power series representation for 2x-4 x2-4x + 3 What is its interval and radius of convergence? Find the Maclaurin series for f(x) (1 z)2 What is its radius of...