Submit script and MATLAB output, i.e., answers, including the graph. Solutions s
ID: 2082438 • Letter: S
Question
Submit script and MATLAB output, i.e., answers, including the graph. Solutions should use MATLAB, except where noted otherwise, and all answers that are not graphs should ALSO be handwritten in ordinary mathematical notation. Handwritten answers in MATLAB notation are not acceptable. Use the "simplify" command where necessary. The "pretty" command may make answers easier to read. (a) Calculate manually the height above the xy-plane of the horizontal circle of intersection of the cone x^2 + y^2 = z^2 and the sphere x^2 + y^2 - z^2 = 8. (b) Draw an ice cream cone by drawing on a single set of coordinates the portion of the sphere above the height of the circle in (a) and the portion of the cone above the xy-plane and below the height of the circle in (a). (a) Find, to four decimal places, the sum Sigma^100_n = 1 (-1)^n/n^2 (b) Find symbolically the exact value of Sigma^infinity_n = 1 1/n^2 For the function f (x, y) = y tan^-1 xy/1 + x62 y^2 find f_zy Find Integral^1_-1 Integral^1 - z_0 (2x + 3y) e^x + y dy dx.Explanation / Answer
clc;
close all;
clear all;
format long
% QUESTION 1
% This requires that both the equations satisfy each other.
% i.e. x^2 + y^2 = z^2 and x^2 + y^2 + z^2 = 8
% This implies z^2 = 8 - z^2 i.e. 2z^2 = 8
% i.e. z^2 = 4 => z = 2 and z = -2.
% Since above x-y plane, Therefore, z = 2.
% Height of intersection = 2
%QUESTION 2.a
syms n x
S2 = symsum(((-1)^n)/(n^2), n, 1, 100);
format short
format compact
double(S2)
%QUESTION 2.a
syms n x
S2 = symsum(1/(n^2), n, 1, Inf)
% QUESTION 4
syms x y
Fn = (2*x + 3*y)*exp(x + y);
intX = int(Fn,x,-1,1);
intY = int(intX,y,0,1-x);
pretty(intY)
%QUESTION 3
syms x y
Fxy = y*atan(x*y)/(1 + (x^2)*(y^2));
simplify(Fxy,'IgnoreAnalyticConstraints',true)