### Limits of Regular Polygons

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Please see the attached file for the fully formatted problem.

Use Taylor polynomials about 0 to evaluate sin(0.3) to 4dp,showing all workings. 1)F(x)=square root 4+x and G(x)=square root 1+x by writing square root of 4+x=2 square root 1+1/4x and using substitution in one of the standard Taylor series, find the Taylor series about 0 for f.Given explicitly all terms up to term in x raise

1) If (bn) is a bounded sequence and lim(an) = 0, show that the lim(anbn) = 0. Explain why Theorem 3.2.3 cannot be used. Note: Here's Theorem 3.2.3 (a) Let X = (xn) and Y = (yn) be sequences of real numbers that converge to x and y respectively, and let c be an element R. Then the sequences X+Y, X-Y, X∙Y, and cX co

Please refer to the attached file for this PERT / CPM problem: I've determined that the critical path for this network is A - E - F and the project completion time is 22 weeks. Here's where I need help: If a deadline of 17 weeks is imposed, what activities should be crashed?

I need a worked solution for these questions (also attached on the LAST PAGE of the attachement. The first couple pages are just examples. Thanks) The structure shown in Figure TA 1 is a pin-jointed section of a canopy and carries a single load of 4 kN acting at the lower right-hand joint. [DIAGRAM] Pin-jointed canopy De

Determine the sum of the integers among the first 1000 positive integers which are not divisible by 4 or are not divisible by 9. (This is not an exclusive or)

Find a formula for a function f, that satisfies the following conditions: 1. lim(x->+/-infinity)f(x) = 0, 2. lim(x->0)f(x) = -infinity, 3. lim(x->3-)f(x) = infinity, 4. lim(x->3+)f(x) = -infinity, 5. f(2) = 0.

1) a) Prove that N ∑ 1/n(n+1) = 1- (1/N+1) n=1 Hence, or otherwise, determine whether the following infinite series is convergent or divergent: b) Determine whether each of these infinite series are convergent or divergent. Justify your an

In 1671, James Gregory, a Scottish mathematician, developed the following series for tan^-1 x {See attachment} 1. Verify that Gregory's series is correct by using a Taylor Series expansion or methods of power series. 2. Find the interval of convergence of Gregory's series. 3. Using Gregory's series, find a series whose

1. Determine whether or not the alternating series converge or diverge.... Please see the attached file for the fully formatted problems.

Let I:=[a,b] be a closed bounded interval and let f:I->R be continuous on I. Then f has an absolute maximum and an absolute minimum on I.

Prove OR disprove the following statements. Explain. (i) There is a nonempty set S in R ( real numbers) such that S contains none of its limit-point(s). (ii) There is a nonempty set S in R such that S is neither open nor closed. (iii) There is a nonempty set S in R such that S is both open and closed. (iv) Let a

A). Prove that the function f(x) = e^x is differentiable on R, and that (e^x)' = e^x. ( Hint: Use the definition of e^x, and consider the sequence of partial sums.) My thoughts on a: I tried to prove the differentiability by proving continuity on R, since e^x is series, sum of polynomials, and all polynomials are different

1. Find the 3rd-degree Taylor polynomial for f(x) = 1/(2+x) at a = 1. 2. Comparison Test let . 3. Comparison Limit let . 4. Comparison Test . Please see the attached file for the fully formatted problems.

Prove or disprove the following statement. Provide detailed answer and justify all steps. 1). There is a nonempty set S in R such that closure of S is equal to R and the closure of its complement closure(R-S) also is equal to R. My thoughts on this problem: Q ( rationals) and R-Q (irrationals), but how to prove that the cl

Let f be a nonnegative measurable function. Show that (integral f = 0) implies f = 0 a.e. See attached document for notations. Please help: This problem is from Royden's Chap 4 text on Lebesgue Integral.

Let's say you work in a company where over 2000 people are employed. Using the Central Limit Theorem, where the mean age of all employed is 37 with a standard deviation of 13; If 5 people are randomly selected, find the probability of their age being less than 22.

1. For each of the sequences whose nth term is given by the formula below (so of course n takes successively the positive integer values 1,2,3...), does it have a limit as n tends to infinity? In each case, briefly explain your answer including justification for the value of the limit (if it exists) a) (1/3)ⁿ b

1- Find the Taylor series generated by f at X = a. f (x) = 1/(10-x) a = 3 2- Find the Maclaurin series for the given functions. A) 1/(6+x) B) sin 10x

Find each limit or explain why it does not exist. Please see attachment.

Each series telescopes. In each case - express the nth partial sum Sn in terms of n and determine whether the series converges or diverges. Please see attachment for full question.

Please assist me with the attached problems, including: 8.7 Find the convergence set for the power series ... 8.8 Given the series (a) estimate the sum of the series by taking the sume of the first four terms. How accurate is the estimate? (b) How many terms of the series are necessary to estimate its sume with three-place

Please assist me with the attached problems, including: 1. Sketch each vector 2. Find the standard representation and length of each vector 3. Maclaurin and Taylor Series and Radius of Convergence See attachment for complete list of questions. Thanks.

The definition of average value of a continuous function can be extended to an infinite interval by defining the average value of f on the interval [a, ∞) to be Lim as t approaches ∞ 1/(t-a)integrand from a to t f(x)dx 1. Find the average value of {see attachment} on [0, ∞). 2. Find the lim as x goes t

1. Test for convergence or divergence, absolute or conditional. If the series converges and it is possible to find the sum, then do so {see attachment} 2. Find the open interval of convergence and test the endpoints for absolute and conditional convergence: {see attachment} 3. For the equation f (x) = ... {see attachment

Thank you in advance for your help; this one sounds like it should be simple, but I still continually get the wrong answer: "Evaluate the limit as x goes to infinity of (1+(3/x))^(4x)."

Real Analysis Let and let be continuous map given by .

Real Analysis Let xEn/n be an irrational number. For each

S(1): Let ε=1, and let any δ>0 be given. S(2): Let n be an integer > max(1, 1/δ), and set x=1/n and y=1/(n+1). S(3): Both x and y belong to (0,1), and |x-y| = 1/n(n+1) < 1/n < δ. S(4): However, |f(x)-f(y)| = |n-(n+1)| = 1 = ε S(5): This contradicts the definition of uniform continuity (i.e.,