### Real Analysis : Cartesian Products and Relations

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

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

Please see the attached file for the fully formatted problems.

Determine whether the integral dx / x^2 which has a an upper limit of 3 and lower limit of -2 converges or diverges. Evaluate the integral if it converges.

Hunter Nut Company produces cans of mixed nuts, advertised as containing no more than 20% peanuts. Hunter Nut Company wants to establish control limits for their process to ensure meeting this requirement. They have taken 30 samples of 144 cans of nuts from their production process at periodic intervals, inspected each can, and

Evaluate lim x => 16 (sqrt(x-4) / x-16)

1. Determine whether the sequence converges or diverges. If it converges, find the limit. If it diverges write NONE.

College level proof before real analysis. Please give formal proof. Please explain each step of your solution. Thank you.

College level proof before real analysis. Please give formal proof. Please explain each step of your solution. If you have any suggestion or question to me, please let me know. Thank you. Please see attached file for full problem description. I. Three real numbers and have the property that . Prove that at least

Suppose that f_k -> f uniformly on (0,1). Let 0 < x < 1. Suppose that lim f_k(t) = A_k for k=1,2,... Show that {A_k} converges and lim f(t) = LIM A_k. That is show lim LIM f_k(t) = LIM lim f_k(t). Where lim represents the limit as t approaches x and LIM represents the limit as k approaches infinity.

1. A piecewise function is given. Use the function to find the indicated limits, or state that a limit does not exist. (a) lim is over x gd - f(x), (b) lim is over x gd + f(x), and (c) lim is over xgd f(x) f(x) = { x^2 - 5 if x < 0 } { -2 if x >= 0 } : d = -3 (a) -5 (b) -2 (c) does not exist

Please see the attached file for the fully formatted problems. Question 1 Differentiate the function f(x) = (a) xlnx - x (b) x5lnx (c) (lnx)2 (d) 1-x ________________________________________lnx Question 2 Figure 2.1 ?(x) = ln ^/¯ (9-x2) ________________________________________(4+x2)

Please refer to the attached file to view the complete questions. ======================================== Question 1 Figure 1.1 y = f(x) = (2x+4)2 - (2x - 4)2 . Apply the slope predictor formula to find the slope of the line tangent to Figure 1.1. Then write the equation of the line tangent to the graph of f at

Let f:[0,1]-->R be a Riemann integrable function. Prove that lim n-->∞ ∫ (from 0 to 1) x^n f(x)dx = 0. I do not know where to begin on this problem. It seems like it should be easy though.

Does there exist a differentiable function f: R-->R such that f'(0) < 0 for all x ≤ 0 and f'(x) > 0 for all x > 0? Give an example of such function or prove that it does not exist.

Let f:[-1,1]-->R be a continuous function such that f(-1)=f(1). Prove that there exists x Є [0,1] such that f(x)=f(x-1).

1.Expand the following function into Maclaurin Series (see attached file) using properties of the power series. 2. The Lagrange interpolation polynomial may be compactly written as is a shape function. Sketch the shape function in a graphic form. 3. Write a forward and backward difference Newton's interpolation formulas b

Please see attached file for full problem description. 1) Consider the series where . Show that and for . 2) Use the result of the previous problem to find . 3) The series converges. Find its sum. 4) Determine whether the series converges or diverges. Fully justify your answer. 5) Determine wheth

Please see the attached file for the fully formatted problems.

Show that there always exist a convergent power series solution to the heat equation with u(x,0)=p(x)=polynomial. Is the solution a polynomial?

Could you please check if the answers are right? Please see the attached file for the fully formatted problems.

Use one-sided limits to find the limit or determine that the limit does not exist. 16-x^2 /4-x lim x => 4 Find the trigonometric limit: sin3x/2x limx => 0 Please show work.

? Find the most general form of the antiderivative of . ? Find the most general form of the antiderivative of . ? Find the most general form of the antiderivative of . ? Find the most general form of the antiderivative of Please see the attached file for the fully formatted problems.

Please see the attached file for the fully formatted problems.

Please see the attached file for the fully formatted problems.

Prove sqrt(x+1) - sqrt(x) goes to 0 as x --> infinity Please see the attached file for the fully formatted problems.

Please see the attached file for the fully formatted problems. I have provided a solution to the attached problem. I do not understand or like the solution - I was hoping you could provide an alternate solution or expand upon the solution I have provided in more detail. Exercise (moment-generating function). ? Let X be

Please see attached file. Graph appropriate functions and then do the limits.

Problem #30, 32, 34, 38 and 40 in both files.

Estimate the value of the limit by filling out a table and then making an educated guess about the tendency of the numbers. Then graph the lim of tanx///x as x approaches 0 to verify own conclusion lim of tanx///x as x approaches o table should be 2 colums with the headings |x|tanx/x|

The function has a limit as f(x) = (1/x) + 3 has a limit of L=3 as x approaches x. This means that if x is sufficiently large (that is if x > N for some number N), the values of f(x) are closer to L=3 than a number epsilon > 0. a) Sketch the graph y=(1/x) +3 and a horizontal strip of points (x,y) such that (if y