Problem 1) Taylor Find first 3 non-zero terms taylor series expansion of (Wolfram Alpha is your friend) ParseError: KaTeX parse error: Can't use function '$' in math mode at position 22: ...= \sqrt{1+e^x} $$ around $x=0$.... 1 Use it to estimate √1+ e¹ along with the bound on uncertainty. Anything sensible counts. 1 Python Python

3. The velocity of a particle which starts from rest is given by the following table. t see) 0 2 8 10 12 14 16 v (fusee) o 12| 16 26 40| 44 25 12 18 Evaluate using trapezium rule, the total distance travelled in 18 seconds.

4. Look up the Pythagorean theorem if you are not already familiar with it. Use the following formula to solve for c in the formula: c = √a2 + b2. Use the proper functions from the cmath header file. Be sure to output the result..

a) Let 1 *dx = 1 = а 4x %3D %3D e 0. Compute the integral using the program trapezoidal.py and, for a given n, let a(n) denote the result. Try to find, experimentally, how large you have to choose n in order for |a – a(n)| < 8 where & = 1/100. b) Recalculate with & = 1/1000. c) Recalculate with & = 1/10,000. d) Try to figure out, in general, how large n has to be such that |a – a(n)| < ɛ for a given value of ɛ. be here to search Shot on OnePlus Powered by Quad Camera

ts) The phase plot for an ODE - f(N) is shown below. (a) Which of these could be a plat of solutions y vs z comresponding to this CDE? A. B. C. D. You can cilck the graphs above to enierge them. OA. A OB. B OC. C OD. D (D) One equilibrium solution af this ODE is y which is chogse and another equilbrium solution of this CDE is y - which is choase (C) For which of the following value(s) of the initial condtion y(0) does the solution g(z) converge as z 00? Select all that apply DA. 0) - 3 OB. 0) - 3.5 OC. p(0) - 2 OD. (0) - -1

(Numerical analysis) Here’s a challenging problem for those who know a little calculus. The Newton-Raphson method can be used to find the roots of any equation y(x)=0. In this method, the (i+1)stapproximation,xi+1,toarootofy(x)=0 is given in terms of the ith approximation, xi, by the following formula, where y’ denotes the derivative of y(x) with respect to x: xi+1=xiy(xi)/y(xi) For example, if y(x)=3x2+2x2,theny(x)=6x+2 , and the roots are found by making a reasonable guess for a first approximation x1 and iterating by using this equation: xi+1=xi(3xi2+2xi2)/(6xi+2) a. Using the Newton-Raphson method, find the two roots of the equation 3x2+2x2=0. (Hint: There’s one positive root and one negative root.) b. Extend the program written for Exercise 6a so that it finds the roots of any function y(x)=0, when the function for y(x) and the derivative of y(x) are placed in the code.

Pyhton Help, As soon as possible You and your friend sell 80 tickets to a raffle. You sold 20 more than your friend. The goal of this problem is to find how many tickets you and your friend have sold. (a) Set up the linear equation for this problem as Ax = b, where x = number of tickets your friend sold. (b) Find A-¹ (Please show your steps). (c) Use A-¹ to solve x. (d) Use python to verify that your A-¹ and solution x are correct. Write your answers for part a here, find the Matrix A from scratch. Write your answers for part b here, please calculate A-¹ manually Write your answers for part c here, x = A-¹b, please perform this calculation manually. [] import numpy as np A = np.array(...) b = np.array(...) [] x2 Fill in the blank in the code cell below for part d, please use your own Python code to replace "..." parts. If you prefer, you can write your piece of code from scratch instead (without filling in the blanks). A_inverse = . Let x₁ represent number of tickets you sold, and x2…

esc 3 A Question 14 of 20: Select the best answer for the question. 14. Use Gauss-Jordan elimination to solve the following linear system: -3x + 4y = -6 5x - y = 10 O A. (2,0) O B. (2,-5) O C. (-6,2) O D. (2,2) O Mark for review (Will be highlighted on the review page) > חח D G $ 4 { 3 R ند 19 F % 50 T Oll SADE A GY O U *∞ C 8 A

4:using numpy to solve the system of linear equations as following x,y,z are variables. 3x+6y+7z = 10 2x+y+8y = 11 x+3y+7z = 22

Evaluating and Solving Radical Functions A person's Body Mass Index is calculated with the formula: BMI=(weight / height2)⋅703 where weight is in pounds and height is in inches. If a person's BMI is above 25 and below 30, they are classified as overweight. If we solve this equation for height, we can determine how tall a person of a given weight should be if they have a BMI of 25.Our new Function is H(w)=√703w / b where H(w) is the person height in inches and ww is a person weight in pounds and b is the person's Body Mass Index (BMI). Use the function to answer the following questions. Determine how tall a person is if they weigh 225 pounds and they have a BMI of 25 Round your answer to one decimal place.The person that weights 225 pounds and has a BMI of 25 is about .......... inches tall. If a person is 68 inches tall and has a BMI of 25, determine their weight.A person that is 68 inches tall and has a BMI of 25 will weigh approximately ........... pounds.