7. Calculate L(f, P) and U(f, P) (as defined in lecture) for the following. Make sure to justify your work, especially...
8. Calculate Lj,P) and UJ, P) (as defined in lecture) for the following. Make sure to justify your work, especially your mi and Mi computations. (a) f(z) =-r, z [0, 1]; an arbitrary partition P = 0. (c) f(z) = sin(z), z e 10, π]; P = {0.5, 뜰자 (d) f(z)= 100 if z#0 (e) f(x) = e", z e 10,1; an arbitrary partition P = {zOR0. Do not -1 if EQ , z e 10, 1]; any partition P...
Please all thank you Exercise 25: Let f 0,R be defined by f(x)-1/n, m, with m,nENand n is the minimal n such that m/n a) Show that L(f, P)0 for all partitions P of [0, 1] b) Let mE N. Show that the cardinality of the set A bounded by m(m1)/2. e [0, 1]: f(x) > 1/m) is c) Given m E N construct a partition P such that U(f, Pm)2/m. d) Show that f is integrable and compute Jo...
11. Here is the Maclaurin series for f(x) = ln(1 +x2): Tm 1-1 r1/3 ln(1 +x2) dz to within 10-6). Use the series to estimate (i.e. 100000 o 0 Show your work and be sure to justify that your estimate has the required accuracy. Circle your estimate. 11. Here is the Maclaurin series for f(x) = ln(1 +x2): Tm 1-1 r1/3 ln(1 +x2) dz to within 10-6). Use the series to estimate (i.e. 100000 o 0 Show your work and...
Exercise 25: Let f: [0,1R be defined by x=0 fx)/n, m/n, with m, n E N and n is the minimal n such that z m/n x- m/n, with m,n E N and n is the minimal n such that x a) Show that L(f, P) = 0 for all partitions P of [0, 1]. b) Let m E N. Show that the cardinality of the set A :-{х є [0, 1] : f(x) > 1/m} is bounded by m(m...
7 points Question 3. An Unusual Integrable Function (Show Working) Consider the function f : 10, 11 → R defined by 1 if r-for some nEN; f(x) = 0 for all other x E [0,1 (1 subpts) (a) Draw a rough diagram of the graph of f. When we study the formal definition of the continuity of a function later in the course, we will be able to prove that this function is discontinuous at those domain values r such...
Show your work. Clearly identify your answer. Justify every step. 1. (5 points) C(x) = 0.0123 - 1.222 +53x gives the cost, in thousands of dollars, to produce u thousand items. (a) Find a formula for the marginal cost. (b) Find and simplify C'(2). What does this number represent? Include units in the description. 2. (5 points) Let f(t) be the temperature of a cup of coffee t minutes after it has been poured. Interpret f(4) = 120 and f'(4)...
The following has you derive the ODE from the Application. For each part make sure you type your answers in the text box using the equation editor and correct notation. rope of length L is attached to the ceiling and makes small vibrations. The displacement from the vertical at any point x is given by u(t, x). Consider a point that is a distance x from the ceiling. Explain why the weight of the cable below this point is given...
signals and communications 2 Make sure you show all working and describe each step in your calculations. 1. A signum function is defined as sgn(t) = { 1、12 0 1 t<0 Plot and express this function in terms of the unit-step function. 5 marks/ Determine and plot the even and odd parts of the signal 2. x(t) (te-3 +2)u(t). 5 marks 3. If prove that y[n-m] = x[n-m] * h[n]. 5 marks 4. Assuming α > 0, plot the signal...
J L M N O P Q R B C D E F G H I 1 Part 2 Cost variance analysis 2 This part relates to Module 23. I have variance analysis support material in the Module 23 folder in course resources. 4 Gourmet, Inc. produces containers of frozen food. During October the company had the following actual production and costs. Actual Containers produced in October 720 Variable Overhead $5,700 Fixed Overhead $13,000 Direct Labor cost $80,000 Which is...
Hello I just need make a review for my work, and I think I did something wrong with the chart, can someone help? Project Description: You work for a design firm that uses many of the software applications in the Adobe Creative Suite, especially Photoshop, Illustrator, InDesign, and Dreamweaver. Your boss has asked you to evaluate whether it would be worthwhile to upgrade the software to the latest version. In addition to reviewing any new or revised features, you also...