Re Consider the function y-932 dy a) Compute the derivative of this function. Do not include...
Q2(a) Find the following derivative of function f(x,y) 0 at point (2, 3). (i) dr dy (2 marks) (ii) dr dx (2 marks) (iii) dxdy (4 marks) (b) Suppose that the volume of water in a tank for time range 0 st 56 is given by function 20) = 10 +51 - (i) Describe, is the volume of water increasing or decreasing at : = 0? (2 marks) (1) Describe, is the volume of water increasing or decreasing at =...
Using the definition, calculate the derivative of the function. Then find the values of the derivative as specified. f(x) = 3 + x2: f'(- 9), F 'O), f (9) Using the definition, calculate the derivative of the function. Then find the values of the derivative as specified. 4 96) = 3. g'(-2), g'(4), g(6) o't)= dx if y = 7x3 dy || s={3 - 4+, t= -6 s'(t)= 0 ne indig y=f(x)= 3 + 14-x, (x,y)= (0,5) The derivative of...
C. This problem is about the inhomogeneous equation dy (1-)2 (1+ x) dy (1-3) (I) y=re +x dr dr2 and the corresponding homogeneous equation dy dy +x dr2 (1- r) (H) -y 0. dr (i) Show that y=r and y= e are solutions of (H). (ii) From (), the general solution of (H) must be y= Ar + Be for arbitrary constants A and B. Solve (I) by the variation of parameters method of Lesson 22, i.e., setting y ur...
Question 1 LO1, PO1 A deflection of a beam is described as dy dy 40d 13y=re dr? dx 1) Solve the general solution. [32 marks] i) Calculate the relationship between y and x using initial conditions | x = 0, y = 0, "v/dt = 0] [8 marks] Enter your answer ON 99+
Find the derivative of the function, NI y=-5(-9x² + 2x) فيا انا dy dx 25( - 9x2 + 2x) -(-18x+2) 2 > > Enter your answer in the answer box A hp
(a) Find the following derivative: d In (5.y dz dB (6 marks) (b) Consider the following bivariate function: g(x,y)exp 8B In (4x2y2)] Find the elasticity of g with respect to x (6 marks) (a) Find the following derivative: d In (5.y dz dB (6 marks) (b) Consider the following bivariate function: g(x,y)exp 8B In (4x2y2)] Find the elasticity of g with respect to x (6 marks)
Exercice 4 (3 pts) Consider D= {(x2 +y?)2 < ry) and compute Vay dr dy Exercice 5 (3pts) Exercice 4 (3 pts) Consider D= {(x2 +y?)2
(a) Find the derivative. y = In(4x – 5) – 3 In(x) dy dx (b) Find the derivative. 4x - y = = In dx State whether the function in part (b) is the same function as that in part (a). The function in part (b) is the same function as that in part (a). The function in part (b) is not the same function as that in part (a).
please explain the steps to your solution using Microsoft excel to Compute the answer 7) From x-1 tox-2, find the values of the function whose derivative is dy Inx) + xy dx using the 2"d order Runge-Kutta approximation and a Ax of 0.1. At x 1, y-1. 7) From x-1 tox-2, find the values of the function whose derivative is dy Inx) + xy dx using the 2"d order Runge-Kutta approximation and a Ax of 0.1. At x 1, y-1.
Consider the differential equation dy -0.5y (y – 4) dt Question 1 Why is the given differential equation considered autonomous?" The derivative of the unknown function(y) is described only in terms of y, not t. The derivative of the unknown function (y) is a first derivative, not a second derivative. The derivative of the unknown function(y) is described only with linear factors such as -0.5y and (y-4), not curves such as sin(y) or 1/y. Question 2 As a step toward...