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Real Analysis

Statistics - 2.1 Calculate the most appropriate measures of central tendency for each variable listed. Show all work. Explain your choices in each case. Discuss what each result means in real terms. ... [See the attached questions file.]

2.1 Calculate the most appropriate measures of central tendency for each variable listed. Show all work. Explain your choices in each case. Discuss what each result means in real terms. A. GNDR B. TRAK C. ADV D. GPA 2.2 Calculate the most appropriate measures of dispersion for each variable listed. Show all work. Explai

Series and Binomial Theorem

See the attached. Q2 a) If the x3, the 3rd term of a series is 3, and x17, the 17th term is -27, state the series. Find if the series has a common difference. b) Coolant hose and nozzle design that to be used on CNC machines, has to ensure that adequate coolant is delivered to the cutter/workpiece interface

Limits and sequences

See attachment a. Use the definition of limits to show that b. Compute the following limits (justify your answers). 1. ( ) 2. c. Let ( be a sequence. Show that ( is convergent if and only if the sequence ( and ( are convergent to the same limit.

Quality Control : Control Limits and p-Charts

Hunter Nut Company produces cans of mixed nuts, advertised as containing no more than 20% peanuts. Hunter Nut Company wants to establish control limits for their process to ensure meeting this requirement. They have taken 30 samples of 144 cans of nuts from their production process at periodic intervals, inspected each can, and

Sequence Convergence and Limit Proof

Suppose {p_n} converges to p. Prove that there is at most one alpha for which the limit as n goes to infinity of |p_n+1-p|/(|p_n-p|^alpha) is a positive finite number. (See attachment for mathematical notation)

Example Functions and Limits Problems

1. Express the distance between the point (3, 0) and the point P (x, y) of the parabola y = x2 as a function of x. 2. Find a function f(x) = xk and a function g such that f(g(x)) = h(x) = 3x + x2 3. Find the trigonometric limit: lim x-tan 2x/sin 2 x → 0

Piecewise Functions, Derivatives and Limits

1. A piecewise function is given. Use the function to find the indicated limits, or state that a limit does not exist. (a) lim is over x gd - f(x), (b) lim is over x gd + f(x), and (c) lim is over xgd f(x) f(x) = { x^2 - 5 if x < 0 } { -2 if x >= 0 } : d = -3 (a) -5 (b) -2 (c) does not exist

Derivatives, Integrals, Limits and Convergence

Please see the attached file for the fully formatted problems. Question 1 Differentiate the function f(x) = (a) xlnx - x (b) x5lnx (c) (lnx)2 (d) 1-x ________________________________________lnx Question 2 Figure 2.1 ?(x) = ln ^/¯ (9-x2) ________________________________________(4+x2)

There are twelve problems involving functions, continuity, finding slope using predictor formula, tangent line to a curve, trajectory of a projectile, finding limits, finding limits using squeeze law and continuity of functions.

Please refer to the attached file to view the complete questions. ======================================== Question 1 Figure 1.1 y = f(x) = (2x+4)2 - (2x - 4)2 . Apply the slope predictor formula to find the slope of the line tangent to Figure 1.1. Then write the equation of the line tangent to the graph of f at

Series Convergence and Divergence

Please see attached file for full problem description. 1) Consider the series where . Show that and for . 2) Use the result of the previous problem to find . 3) The series converges. Find its sum. 4) Determine whether the series converges or diverges. Fully justify your answer. 5) Determine wheth

Trigonometric Limits

Use one-sided limits to find the limit or determine that the limit does not exist. 16-x^2 /4-x lim x => 4 Find the trigonometric limit: sin3x/2x limx => 0 Please show work.

Difference Quotient : Limits and Differentiable Functions

Assume f:(-1,1) --> R and f'(0) exists. If a_n , b_n -> 0 as n->infinity, define the difference quotient: D_n = ( f(b_n) - f(a_n) ) / ( b_n - a_n). a) Prove lim [n -> infinity] D_n = f'(0) under each condition below: (i) a_n < 0 < b_n . (ii) 0 < a_n < b_n and (b_n) / (b_n - a_n) <= M (iii) f'(x) exists and is contin

Measure Theory and Dominated Convergence Theorem

Please see the attached file for the fully formatted problems. I have provided a solution to the attached problem. I do not understand or like the solution - I was hoping you could provide an alternate solution or expand upon the solution I have provided in more detail. Exercise (moment-generating function). ? Let X be

Function of Limits

The function has a limit as f(x) = (1/x) + 3 has a limit of L=3 as x approaches x. This means that if x is sufficiently large (that is if x > N for some number N), the values of f(x) are closer to L=3 than a number epsilon > 0. a) Sketch the graph y=(1/x) +3 and a horizontal strip of points (x,y) such that (if y

Analysis: Finding a Limit

Find limit x>> -1^+ f(x) f(x)= x - 2, for x <= 3; x - 1, for x > 3 Also: When you first begin to draw the graph of f(x), why do you start where you do? How high do I go when drawing a graph? How do I know when to stop?

Limit

Evaluate the limit: lim x cot x x&#8594;0

Business Statistics

These problems may or may not need PHSTAT again. All is the same as priors posting the responses in a MS Word document. Attached are: -Problems [MS Word] -Spreadsheet [Excel]

Some problems on network models

I have attached some quantitative Analysis Questions that I need help solving so I can add to my study guide. The book used was Quantitative analysis for Management by Barry Render but as you already know these concepts are found in any Quantitative Analysis book.

Remainder Estimation Theorem and Euler's Formula

1.) Given that 1-x+x^2+...+(-x)^n is a power series representation for 1/(1+x), find a power series representation for (x^3)/(1+x^2). 2.) The Maclaurin series for f(x) is: 1+2x+((3x^2)/(2))+((4x^3)/(6))+...+(((n+1)x^n)/(n!))+... Let h(x)= (the integral from 0 to x) f(t) dt. Write the Maclaurin series for h(x).

Taylor Series and Systems of Vector Equations

1 Write the Taylor series with center zero for the function f(x) = ln(l+x^2). 2 Given a =2i +3j, b = 3i +5j , and c = 8i + 11j express c in the form ra+ sb where r and s are scalars.

Real Analysis: Set Measures and Measurability

9. Let F be a closed subset in R, and ... the distance from x to F, that is, ....... Clearly, ....) whenever .... Prove the more refined estimate .... for a.e. xEF, that is,..... [Hint: Assume that x is a point of density of F.] Please see the attached file for the fully formatted problems.

Limits: True or False

Please help with the following problem. Provide step by step calculations. True or false: a)lim x--->2- f(x) = 3 b)limx--->2+ f(x) =0 c)lim x--->2- f(x) = lim x--->2+ f(x) d) lim x--->2 f(x) exists e) lim x--->4 f(x) exists f) lim x--->4 f(x) = f(4) g) f is continuous at x=4 h) f is continuous at x=0 i) lim x--->3

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

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

Find the radius of convergence and interval of convergence of power series.

1. Find the radius of convergence and interval of convergence of series. 2. A function f is defined by f(x) = 1+ 2x + x^2 + 2x^3 +x^4+...... that is, its coefficients are =1 and =2 for all n> =0. Find the interval of convergence of the series and find an explicit formula for f(x). 3. Suppose the radius of convergen