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Real Analysis

Find limits

A) Find lim x---> 2+ C(x) b) Find lim---> 2- C (x) c) Find lim x---> 2 C (x) d) Find C (2) e) Is C continuous at x=2? At 1.95? See attached file for full problem description.

Limits : L'Hopital's Rule

Please see the attached file for the fully formatted problems. keywords : find, finding, calculating, calculate, determine, determining, verify, verifying, evaluate, evaluating, calculate, calculating, prove, proving, L'Hospital's, L'Hospital


Evaluate the limit: (x^2)/(ln[x]) as x approaches positive infinity. keywords: finding, find, calculate, calculating, determine, determining, verify, verifying, evaluate, evaluating

Real Analysis : Norms and Bounded Sets

8. Fix an n-dimensional real vector space V with n a positive integer greater than 1. If you want to take V to be R, fine. Consider non-empty open sets B C V with the following properties: (a) B is bounded and convex (contains the line segment through any two of its points); (b) If VEB,then there is a number t0>0 for which tv

Taylor Series Expansions, Residues and Larent Series

A) Give the infinite Taylor series expansions for the three functions e^z, sin z, cos z. b) Write 5 nonzero terms, including the one that determines the residue, for the Laurent series of e^z / z^4 centered at 0.

Computing U, H, F, G, S, and mu for nitrogen gas.

For a mole of nitrogen (N_2) gas at room temperature and atmospheric pressure, compute the internal energy, the enthalpy, the Helmholtz free energy, the Gibbs free energy, the entropy, and the chemical potential. The rotational constant epsilon for N_2 is 0.00025 eV. The electronic ground state is not degenerate.

Finding a Limit using Riemann Sums

Evaluate (lim)(sin(Pi/(n))+sin((2*Pi)/(n))+sin((3*Pi)/(n))+***+sin((n*Pi)/(n)))/(n) by interpreting it as the limit of Riemann sums for a continuous function f defined on [0,1]. keywords: integration, integrates, integrals, integrating, double, triple, multiple

Convergence of Power Series

1 Determine whether the series converges absolutely, converges conditionally, or diverges. ∞ Σ 2∙4∙6∙∙(2n)/2ⁿ(n+2)! n=1 2 Calculate sin 87° accurate to five decimal places using Taylor's formula for an appropriate functio

Determine whether the series is convergent or divergent.

Determine whether the series is convergent or divergent: a) ∑ from n = 1 to ∞[ 1/nlnn] b) ∑ from n = 1 to ∞ [1/sqrt(n^2 + 1)] c) ∑ from n = 1 to ∞ [cos^2n/ n^2 + 1] d) ∑ from n = 1 to ∞ [2 + (-1)^n/nsqrt(n)] 2) a) use the sum of the first 10 terms to estimate the sum of the ser

Power Series Proof

Define the set R[[X]] of formal power series in the indeterminate X with coefficients from R to be all formal infinite sums sum(a_nX^n)=a_0 +a_1X+a_2X^2+... Define addition and multiplication of power series in the same way as for power series with real or complex coeficients,i.e extend polynomial addition and multiplication t

Limits and Inderterminate Forms

Evaluate the limit, using L'Hospital Rule if necessary. lim sinax/sinbx as x approaches 0 lim ln x^4/x^3 as x approaches infinity

Vectors and Limits

See attached file for full problem description. 1) Find the canonic equation of the straight (recta) in the space( espacio), with R 2) Calculate the scaling product of the vectors r y s knowing that r = 3i + 4j; that the module of the vector / s/ = 6; and the angle that both vectors form is 120° 3)Find

General Vector Taylor Series Expansion: Measure of deviation

2. Arfken, p. 342, 5th Ed. (p. 359, 6th Ed.), ) Prob. 5.6.7. Use the General Vector Taylor Series Expansion For a General Function, cI) (r) = (I) (x, y, z) , Of a Three-Dimensional Vector Coordinate, Expressed In Cartesian Coordinates, which is Expanded About the Origin, r = 0 Or x = y = z = 0 , Where 0(0 = (1)(x', y', z') 1 ir,

Stone-Weierstrass Approximation Theorem

Show that there is a countable set F of functions of form x--->a_0 + a_1cosx + a_2cos(2x) + ... +a_ncos(nx) such that every continuous real-valued function on [0,pi] is the uniform limit of a sequence of functions (f_n) in F.

3-Sigma Control Limits

Jim Outfitters makes custom fancy shirts for cowboys. The shirts could be flawed in various ways, including flaws in the weave or color of the fabric, loose buttons or decorations, wrong dimensions, and uneven stitches. Jim randomly examined 10 shirts, with the following results: Shirt Defects 1 8 2 0 3 7 4 12 5 5 6 10