Please see the attached file for full problem description. a) Evaluate b) What is the radus of convergence .... .... To what simple function does this series converge? c) Is f(z)=... ... analytic near z= -1? and expand f(z)= ... in a power series near z= -1 can we predict the domain of convergence from the outset?
Please see the attached file for the fully formatted problems. Suppose that is not a perfect nth power, i.e K is not equal to (a) Prove that is not a member of Q, the set of all rational numbers. (b) Infer that the nth root of a natural number is either a natural number or it is irrational.
Please see the attached file for full problem description.
Antiderivative of: (t5 + 6t3) dt
See attachment
See the attached a word document. Be sure to show me all of your work so that I can fully understand how to do the problems correctly.
Show that the sum from 0 to infinity of (1-x)x^n does not converge uniformly on [0,1]. What subintervals of [0,1] does it converge uniforlmly on?
Please see the attached files for the fully formatted problems.
What is the fifth term of the series an = n + an-1' if a0 = -3.
Find an article through newspapers, magazines, professional journals, etc and find at least two examples of data that are best modeled using linear formulae. Describe the importance of each example and why a linear model is appropriate for the data. Note that we are referring to a linear model not simply a time chart where dots
Write out the Riemann Sum for R(f,P, 0, 2) for arbitrary n, f(x) = x2+/-3x+2, where each ∆xk = 2/n and ck = xk, simplify and use the formulas ∑n,k=1 k=(n(n+1))/2 and ∑n,k=1 k2=n((n + 1)(2n + 1))/6 to find the limit as n --> 1.
See attached lim (sin^2 3t)/2t t--->0
Please see the attached file for the fully formatted problem. Lim (1 - cos t)/2t t--> 0
See attached.
Evaluate Limit[tan (a*theta)/sin(b*theta)] as theta approaches zero.
Calculate limit (1/x^2) as x approaches infinity
Prove that Lim (3x)=6 as x approaches 2 using Epsilon-Delta definition.
Define a limit graphically
Determine whether the series Sum(n!/n^n) n=1..infinity is absolutely convergent, conditionally convergent or divergent.
Find lim (ln x)^3/(x) as x--> infinity
Lim (x+1)^(1/X) X->0
Test the series (in the attached file) for convergence or divergence by using the Comparison Test or the Limit Comparison Test.
Please see the attached file for the fully formatted problem. What is the maximum of F = x1 +x2 +x3 +x4 on the intersection of x21 +x22 +x23 + x24 = 1 and x31+ x32+ x33+ x34= 0? As this is an analysis question, please be sure to be rigorous and as detailed as possible.
The question is in attached file. Suppose a sequence of continuous functions, { ?n }, has the property that ?n  ? and  > 0,   > 0 such that if | x - y | <  then n, | ?n (x) - ?n (y)| <  Prove that ? is continuous.
Let Æ’n : R2 ï‚® R be Æ’n (x,y) = (x+y) / n a. Show that Æ’n ï‚® 0 , but convergence is not uniform. b. Show that the convergence Æ’n ï‚® 0 is uniform on bounded sets.
Summation Series. See attached file for full problem description.
Verify Fubini's Theorem for an integral evaluated over an equilateral triangle. (My notes from class-make a function up, similar to something used in question 1, but change powers of x & y.) You should discuss fully the reasons for the limits of integration in your solution.
I have managed to evaluate the double integral using the horizontal simple method, and answer 63. But when I reverse the order (vertical simple method) I cannot reach the same answer of 63, I get 65. 1) Evaluate the double integral of f(x,y)=x+4y^2 over the triangular region with vertices (-2,2) (4,2) & (1,-1) Check that r
Let f(x) be integrable on [a,b], and let g(x) be nondecreasing and continuously differentiable on [a,b]. Let {p be element of P} be a partition of [a,b], and define U(f,g,p) = SIGMA (Mi(g(the ith term of x) - g(the (i-1)th term of x))) as i=1 to n L(f,g,p) = SIGMA (Ni(g(the ith term of x)-g(the (i-1)th term of x))) as i=1 t
I need a proof for "If f on [a,b] is continuous & 0 is not a member f([a,b]) then f is bounded away from 0."