Hint: use geometric series and the theorem on differentiation of a power series 6.7 Obtain power...
Math 181 Worksheets W16 * for <1, to find a power series representation 3. Use the geometric series for the following functions. (a) sw) - (a) f(x) = 1+ 60 Etoje (x)" (b) 9(2) - T- + sa www. in a lot (x)} (14 x 31k (a) Wr) = (e) What are the radii of convergence of the power series above?
(1 point) Find a function of x that is equal to the power series En= n(n + 1)x" = for <x< Hint: Compare to the power series for the second derivative of 1-X (1 point) Find a formula for the sum of the series (n + 1)x" n=0 101+2 for –10 < x < 10. Hint: D,( *) = " " 10n+1
Use the power series 1 1 + X = Ë (-1)^x), 1x! < 1 n=0 to find a power series for the function, centered at 0. 1 g(x) x + 1 00 g(x) = Σ n=0 Determine the interval of convergence. (Enter your answer using interval notation.)
1 6. Using the power series = Σ c" |x | < 1, find a power series about O for 1 х n=0 1 and state the radius of convergence. (2 - x)2
A) B) C) 1 Find the Laurent series for 22 +22 for 0 < 121 < 2 Find the Laurent series for (z+2)}(3-2) for 2 – 3) > 5 1 Find the Laurent series for z2(z-i) for 1 < 12 – 11 < V2
5. Use the Standard Normal Distribution table to find P (Z<-0.69)
1. Prove that log(1+r) = geometric series. (-1)-1 for <1. The simplest way to do this is to integrate the
Problem 1 Geometric Series. We will need to sum the geometric series to simplify some of the partition functions developed in class. Prove that the geometric series 7:0 for r| < 1. You may find it helpful to consider the partial sums Sj ?, xk 1+1+-.+4 and rSi =x+x2 + +z?+1 take the limit J ? 00, Can you see why the geomet ric series converges for r < 1 and diverges for ll 2 1 Explain. . You will...
Use the Mean Value Theorem to demonstrate that In(1 + x) < x, given that x > 0.
Let F = < - yz, 12, my >. Use Stokes' Theorem to evaluate || curiF . d5, where S is the part of the paraboloid z = 13 – 2? - y that lies above the plane z = 12, oriented upwards Preview Get help: Video License Points possible: 1 This is attempt 1 of 3. Submit