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# Real Analysis

### Business Math : Price Index, Dara Analysis, Return on Investment (ROI), Inventory and Expenses

12. Key Question The following table shows nominal GDP and an appropriate price index for a group of selected years. Compute real GDP. Indicate in each calculation whether you are inflating or deflating the nominal GDP data. Year Nominal GDP Billions, Price Index (1996 = 100) Real GDP, Billions 1960 \$ 527.4 22.19 \$____ 19

### Real numbers analysis

A. let f(x):= 1/(x^2), x does not equal zero, x elements of Reals determine the direct image f(E) where E= {x elements Reals: 1<=x<=2} determine the inverse image f^-1(G) where G= { x element of Reals: 1<=x<=4} b. show that if a<b then a< 1/2(a+b)<b c. for a,b,c elements of reals with a<b, find an explicit bijection of

### Mathematics of Flight Time

Two planes leave O'Hare Airport in Chicago at the same time.One flies directly east at 540 miles per hour.The other flies directly west at 720 miles per hour.How long will it take them to be 1890 miles apart.

### Power series solution

Compute the power series solution for the ODE y''+x^2y=0 and determine the radii of convergence for the two series solutions.

### Suppose an economy's real GDP is \$30,000 in year 1 and \$31,200 in year 2. What is the growth rate of its real GDP?

1. Compute the real GDP when provided the nominal GDP and an appropriate price index for a group of selected years. 2. Suppose an economy's real GDP is \$30,000 in year 1 and \$31,200 in year 2. What is the growth rate of its real GDP? Assume that population is 100 in year 1 and 102 in year 2. What is the growth rate of GDP pe

### Effect of Changing a Company's Credit Terms

The Dunstill company has obtained the following information: ? Annual Credit Sales= 30 million ? Collections period is= 60 days ? Credit terms= Net 30 days ? Interest rate = 12% The company is considering changing its credit terms to 4/10 net 30. The company anticipates 50% of the customers will take advantage of this poli

### Cluster point proof

Prove that a set S included R has no cluster points if and only if S intersection [-n,n] is a finite set for each n in N.

### Convergent Sequences and Limits

Suppose {an} is a convergent sequence and {bn} is a sequence with the property that bn < an if n is even and bn > an if n is odd. Does bn converge? Determine the limit of the given sequence (2 problems). (3n^3+2n+1)/(5n^2-2*n+3) 1/[1+(n^3 / 3^n)] Please see the attached file for the fully formatted problems.

### Antiderivatives

There are two incircled questions attached. The graph of a function of f is shown. Which graph is an antiderivative of f and why? Find the antiderivative F of f that satisfies the given condition.

### Limits & L'Hopital's Rule

Help with attached incircled questions #28 #32 and #40. Find the limit. Use L'Hopital's rule where appropriate...

### Constant Limits Exists

Find a constant K so that the limit exists. lim x^2 + 3x + 5 / x^K + 3 x--> infinity x^.. means to the power of Please show work. Please no power points. Thank you.

### Limit Equal to One

See attached page for limit Find the path on which the given limit is equal to one

### Limits

See attached page for problems Find the limit, if it exist, or show that the limit does not exist.

### Mathematics - Sensitivity Report Analysis

Excel Sensitivity Analysis {please see the attached file}

### 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

### Equation Factors Demonstrated

Insert the required factor and demonstrate how you arrived at your solution. (4x+5)/(x^2 +3x+4)^3=(___)(1/( x^2 +3x+4)^3))*(8x+10)

### Power series

See attached Use a power series method to find the complete solution of...

### Radius of convergence and sum of series

Determine the radius of convergence of the series... (see attachment)

### Find the Sum of a Series to Infinity

Find the sum, if possible of the following series (see attached).

### 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

### Sequences and Convergence

1. Define the following sequence a. Show that and are monotone sequences. b. Show that and converge to the same limit. c. Find . d. If for some . Is ( ) still convergent. (See attachment).

### 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.

### Power and Maclaurin Series

Find a power series representation for the function f(x) = 1/x^4 + 1 and determine the interval of convergence. Use a known Maclaurin series to derive the Maclaurin series of the function g(x) = e^-x/x. Evaluate the indefinite integral (integral) e^-x/x (dx) as an infinite series.

### How do you find the sum of the series?

Give the sum of the following series: a. SUM(as n=1, goes to infinity) pi^n / 4^n_1 b. SUM(as n=1, goes to infinity) 1/(n+1) - I/n Indicate whether the following series are convergent or divergent. Indicate the test you apply to support your conclusion. a. SUM(as n=1, goes to infinity) 2/(n-1) b. SUM(as n=2, goes

### Definition of Maclaurin Series

Find the Maclaurin series for f(x) using the definition of a Maclaurin series. (Assume that f has a power series expansion. Do not show that Rn(x) --> 0) Also find the associated radius of convergence. f(x)= ln(1+x) Please show steps.

### Computing Trouble Limit Methods

I am having trouble computing these limits. Please specify the method used in computing and detailed instructions.

### Taylor Series Expansions

Use Taylor Series Expansions to find lim x->0 (cosx - 1 + (x^2/2))/x^4

### Differentiability and Limits

Decide whether each of the following statements is true or false. If true, explain why. If false, give a counter-example and explain why the counter-example contradicts the statement. Suppose F(x) is differentiable at ALL x in R. Suppose lim x->0 f '(x) = L, does it follow that f '(0) = L?

### Real Analysis : Cartesian Products and Relations

College level proof before real analysis. Please give formal proof.