Starting from mynewton write a function program mysymnewton that takes as its input a symbolic function f and the ordinary variables x0 and n. Let the program take the symbolic derivative f ′ , and then use subs to proceed with Newton’s method. Test it on f(x) = x 3 − 4 starting with x0 = 2. Turn in the program and a brief summary of the results

Let f be a function with domain the reals and range the reals. Assume that f has a local minimum at each point x in its domain. (This means that, for each x ∈ R, there is an E = Ex > 0 such that, whenever | x−t |< E then f(x) ≤ f(t).) Do not assume that f is differentiable, or continuous, or anything nice like that. Prove that the image of f is countable. (Hint: When I solved this problem as a student my solution was ten pages long; however, there is a one-line solution due to Michael Spivak.)

1. Must be nicely written up AS A PROOF.

a. Show that gcd(m + n, m) = gcd(m, n).

b. If n | k(n + 1), show that n | k.

c. Show that any two consecutive odd integers are relatively prime.

A body of mass 7 kg is projected vertically upward with an initial velocity 18 meters per second. The gravitational constant is g=98m/s². The air resistance is equal to k|v| where k is a constant.

Find a formula for the velocity at any time ( in terms of k ):

Find the limit of this velocity for a fixed time t₀ as the air resistance coefficient k goes to 0.

Given a scalar fifield φ(x, y, z)=3x²-yz and a vector field F(x, y, z)=3xyz²+2xy³j-x²yzk.

Find:

(i)F.∇φ.

(ii)F×∇φ.

(iii)∇(∇.F).

100 kg of R-134a at 320 kPa are contained in a piston-cylinder device whose volume is 7.530 m³. The piston is now moved until the volume is one-half its original size. This is done such that the pressure of the R-134a does not change. Determine the final temperature and the change in the total internal energy of the R-134a. (Round the final answers to two decimal places.)

Analyzing Transactions Using the Financial Statement Effects Template Following are selected transactions of Mogg Company. Record the effects of each using the financial statement effects template. Shareholders contribute $10,000 cash to the business in exchange for common stock. Employees earn $500 in wages that have not been paid at period-end. Inventory of $3,000 is purchased on credit. The inventory purchased in transaction 3 is sold for $4,500 on credit. The company collected the $4,500 owed to it per transaction 4. Equipment is purchased for $5,000 cash. Depreciation of $1,000 is recorded on the equipment from transaction 6. The Supplies account had a $3,800 balance at the beginning of this period; a physical count at period-end shows that $800 of supplies are still available. No supplies were purchased during this period. The company paid $12,000 cash toward the principal on a note payable; also, $500 cash is paid to cover this note's interest expense for the period. The company receives $8,000 cash in advance for services to be delivered next period. Use negative signs with your answers, when appropriate. Hint: For transaction 4, enter the net effect amount for balance sheet answers.

Question 1. State the prove The Density Theorem for Rational Numbers.

Question 2. Prove that irrational numbers are dense in the set of real numbers.

Question 3. Prove that rational numbers are countable

Question 4. Prove that real numbers are uncountable

Question 5. Prove that square root of 2 is irrational

Question 1. State the prove The Density Theorem for Rational Numbers.

Question 2. Prove that irrational numbers are dense in the set of real numbers.

Question 3. Prove that rational numbers are countable

Question 4. Prove that real numbers are uncountable

Question 5. Prove that square root of 2 is irrational

If V is a linear space and S is a proper subset of V, and we define a relation on V via v1 ~ v2 iff v1 - v2 are in S, a subspace of V. We are given ~ is an equivalence relation, show that the set of equivalence classes, V/S, is a vector space as well, where the typical element of V/S is v + s, where v is any element of V.

Briefly describe the main similarities and differences between the threshold phenomena for the stochastic general epidemic model and the deterministic general epidemic model.

(Topic: Epidemics)

Pls explain in a simple way to understand. Thxs

Write a MATLAB code to obtain the following. Keep your code commented whenever required. Copy your source code and command widow outcomes and screen shots of any plots in your solution.

Develop three functions for temperature-conversion.

• Create a function called F_to_K that converts and return temperatures in Fahrenheit to Kelvin and store results in ‘F_to_K2.txt’.
• Create a function called C_to_R that converts and return temperatures in Celsius to Rankine and store results in ‘C_to_R2.txt’.
• Create a function called C_to_F that converts and return temperatures in Celsius to Fahrenheit and store results in ‘C_to_F2.txt’.

Use the following equations to achieve these conversions.

1 degree Fahrenheit =255.928 Kelvin

1 degree Celsius =493.47 Rankine

1 degree Celsius =33.8 degrees Fahrenheit

• Write an appropriate MATLAB code to collectively call and test these functions.
  • It should import data from ‘Tempr2.txt’ and convey it to each of the above mentioned user defined functions. ‘Tempr2.txt’ is available on BlackBoard under the folder Final_Exam.
  • It should display on the command window one conversion table for each case while displaying first 20 inputs and converted values.
  • It should also display a table on the command window, which presents the mean, median, variance and standard deviation values according to the following Table.