### Limit

See attached page for limit Find the path on which the given limit is equal to one

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See attached page for limit Find the path on which the given limit is equal to one

Excel Sensitivity Analysis {please see the attached file}

2.1 Calculate the most appropriate measures of central tendency for each variable listed. Show all work. Explain your choices in each case. Discuss what each result means in real terms. A. GNDR B. TRAK C. ADV D. GPA 2.2 Calculate the most appropriate measures of dispersion for each variable listed. Show all work. Explai

Insert the required factor and demonstrate how you arrived at your solution. (4x+5)/(x^2 +3x+4)^3=(___)(1/( x^2 +3x+4)^3))*(8x+10)

Determine the radius of convergence of the series... (see attachment)

Find the sum, if possible of the following series (see attached)

See the attached. Q2 a) If the x3, the 3rd term of a series is 3, and x17, the 17th term is -27, state the series. Find if the series has a common difference. b) Coolant hose and nozzle design that to be used on CNC machines, has to ensure that adequate coolant is delivered to the cutter/workpiece interface

1. Define the following sequence . a. Show that and are monotone sequences. b. Show that and converge to the same limit. c. Find . d. If for some . Is ( ) still convergent. (see attachment)

Find the Maclaurin series for f(x) using the definition of a Maclaurin series. (Assume that f has a power series expansion. Do not show that Rn(x) --> 0) Also find the associated radius of convergence. f(x)= ln(1+x) Please show steps.

I am having trouble computing these limits. Please specify the method used in computing and detailed instructions.

Use Taylor Series Expansions to find lim x->0 (cosx - 1 + (x^2/2))/x^4

Decide whether each of the following statements is true or false. If true, explain why. If false, give a counter-example and explain why the counter-example contradicts the statement. Suppose F(x) is differentiable at ALL x in R. Suppose lim x->0 f '(x) = L, does it follow that f '(0) = L?

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.