### 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¯¯¯

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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¯¯¯

Please see the attached file for the fully formatted problems.

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]

Find the Taylor series expansion for the function for the given value of a. F(x) = √ x, a= 4

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

F(x) = sin 4x

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.)

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.

3. Southland Corporation's decision to produce a new line of recreational products resulted in the need to construct either a small plant or a large plant. The selection of plant size depends on how the marketplace reacts to the new product line. To conduct an analysis, marketing has decided to view the possible long-run dema

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

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.

Determine the set of points at which the function is continuous. 27. F(x, y) = sin(xy)/(e^x - y^2) Use polar coordinates to find the limit. [If (r, theta) are polar coordinates of the point (x, y) with r >= 0, note that r --> 0+ as (x, y) --> (0,0).] lim (as (x,y) --> (9,0)) of (x^3 + y^3)/(x^2 + y^2) Use spherical

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).

1- prove : 1/2^2 + 1/3^2 +1/4^2+ ..... + 1/n^2 < 1

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.

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.

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.

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.

Let f1,...,fk be continuous real valued functions on the interval [a,b]. Show that the set {f1,...,fk}is linearly dependent on [a,b] iff the k x k matrix with entries b <fi,fj> = ∫ fi(x)fj(x)dx has determinant zero. a See attached file for full problem description.

Let fn(x) = cos(nx) on R. Prove that there is no subsequence fnk converging uniformly in R. Please see the attached file for the fully formatted problems.

I have to find the radius of convergence for the following series: Sum from j = 0 to infinity of z^(3j)/2^j, and the answer according to my book is R = 2^(1/3).

I must use the ratio test to show that the following series converges: ∞ Σ (k^2 + i)/(k+i)^4 k=1

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 ___ __ ___

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. See attached for full problem description.

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

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