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Real Analysis


Find the limit lim 3e^2x - 3 x→0 ¯¯¯¯x¯¯¯¯ by recognizing it as a derivative f'(a) of the appropriate function at a suitable value of a. Please specify the function f in the answer - numerical computation of the limit is not enough. (^ means exponent and 3e^2x - 3 is over x)

Finding Limits

Find the limit lim cos x x→∞ ¯¯x¯¯¯ (cos x is over x - I am not able to make a continuous line)


Please explain the steps and solutions, thanks: Evaluate the limit: lim (1+ x)^1/x x→∞ (^ means exponent and 1/x is the exponent)


Evaluate the limit: lim x cot x x→0


Find the limits and justify the answers: a) lim √xlnx x→0^+ b) lim (1+2x)^1/x x→0^+ (^ means exponent and ^1/x is the exponent 1 over x)


A) lim 3x x→0 ‾‾‾‾‾‾‾ = 3 x^2+x b) lim x does not exist because one cannot divide by 0 x→0 ‾‾‾‾‾‾ x^2+x c) If f (5) is not de

Evaluating Functions and Limits

H is a function such that h(0) = 1, h(2) = 7, h(4) = 5, h'(0) = -2, h'(2) = 3, and h'(4) = -1 Evaluate lim h(w)−1 w→0 ¯¯¯w¯¯¯

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]

Maclaurin Series Expansion

Evaluate the Maclaurin series expansion using the first three nonzero terms: 1 ∫ (cos x - 1)/x dx 0 keywords: integrals, integration, integrate, integrated, integrating, double, triple, multiple

Sums of Convergent Series

How many terms of the convergent series do you need in order for the partial sum Sn to estimate the actual sum of the series correctly to four decimal places? ( The sum of the series from n=1 to infinity of (-1) ^5n divided by Ln n.)

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.

Terms of Power Series

4. Let f be the function by f(x)e^(-2x^2) a. Find the fist four nonzero terms and the general term of the power series for f(x) about x = 0. b. Find the interval of convergence of the power series for f(x) about x =0. Show the analysis that leads to our conclusion. c. .... Please see the attached file for the fully formatted

Convergence and Divergence of Series

Page Number: - 568 1 / (b, e, g, h) Page Number :- 576 1 / (c, d), 5 / ( a, c, d, f) Page Number: - 579 1 /( e , f, h), 3 Please explain all steps.

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 : Absolutely Continuous

See attached file for full problem description. Problem 4 Only. If f:[a,b]-->R is absolutely continuous then |f(e)| = 0 for all E ⊂ [a,b] with |E| = 0.

Power Series and Radius of Convergence

Consider the power series ∑anxn for which each coefficient an is an integer. Prove that this series has a radius of convergence, R, where either R=positive infinity or R≤1 See attached file for full problem description.

Sequences and Limit Superior

Suppose that xn x and the sequence (yn) is bounded. Show that ___ ___ lim (xn + yn) = lim xn + lim (yn). ___ I know that since (xn) converges lim xn = lim (xn) and that ___ __ ___

Taylor Series

Write the Taylor series about x=0 for ([cos(X^3)]/x) and ([cos(7X)]/x^3) I would like to see the step by step process for how this works. I know the standard series for any variable of cos(x), but would like to understand how dividing by x changes the problem keywords : find, finding, calculating, calculate, determine,


Please explain how/why: lim x---> - 4 x^2 - x - 20 / x+4

Find Limit

Find Limit. See attached for full problem description.

Limits: True or False

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 f(x) = lim x--->5 f(x) j) f is continuous at x = 2 See attached file for d