### 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.

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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.

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

1. Express the distance between the point (3, 0) and the point P (x, y) of the parabola y = as a function of x. 2. Find a function f(x) = and a function g such that f(g(x)) = h(x) = 3. Find the trigonometric limit: . 4. Given , use the four step process to find a slope-predictor function m(x). Then write an eq

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

Fix R>0. Show that, if n is large enough, then P_n(z)=1+z+z^2/2!+z^3/3!+...+z^n/n! has no zeros in {z:|z|<=R}

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

Please see the attached files for the fully formatted problems. This problem is from Introduction to Analysis (Maxwell Rosenlicht).

What is the nth term for the following: 1, 1/2, 3, 1/4, 5, 1/6.

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.

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.

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

Determine the convergence or divergence of the series. See attached file for full problem description. ∞ Σ (n+1)/(2n-1) n=1

3. A piece of electronic equipment used for aviation has three elements connected in series, or sequence. The reliability of each of the three elements is as follows: Element A: 0.92 Element B: 0.94 Element C: 0.91 a) Draw how these three elements are connected. b) What is the r

Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges find its limit. an = (n-2)!/n!

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: 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

Show that the function h, defined on I by h(x)=x for x rational and h(x)=0 for x irrational, is not Riemann integrable on I.

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

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

Determine whether the sequence converges or diverges. If converges find the limit. A) an = (n + 2)!/n! B) {n^2e^-n} C) an = ln(2n^2 + 1)-ln(n^2 + 1) D) an = cos^2n/2^n

Please find attached problems to solve in ps2.doc file. The tables are in the tables.zip file. The solutions by another student are in the pdf file in the zip file attached. The other ms excel files are also there. Please check the solutions up. If the solutions are fine then you can submit a response with any comments or

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

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,

Show that (a) sin x = summation (0-infinity) (-1)^n x^(2n+1)/(2n+1)! (b) cos x = summation (0-infinity) (-1)^n x^(2n)/(2n)! Use the Taylor series expansion around the origin, f(x) = summation (0-infinity)[x^n/n!]f^n(0), and derive the power series expansions for sin x , cos x and e^x. Then write out the first few real

Determine the lower bound for the radius of convergence of the series solution about x y'' + 4y' + 6xy = 0, x=1

Determine whether or not each of the following limits exists. Discuss also the continuity of each of the following functions at given point c. Give reasons to your answers. Please see the attached file for the fully formatted problems.

Discuss the convergence and the uniform convergence of each of the following sequences of functions on the given set D. Give reasons to your answers: a) f_n(x) = (x/n)e^(-x/n), D = [0, infinity) b)f_n(x) = (x^n)/(1 + x^2n), D = [2, infinity)

Prove that if for each natural number, n, the function f_n on I = [0,1] ---> the reals is monotone increasing and if f(x)=limit as n--->infinity of f_n(x) is continuous on I, then the convergence is uniform on I.

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.

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