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Problem #16: [2 marks] A solution, y = f(x), of the differential equation, x²y + 5x²y = xt has f(0) = }. What is f(1)? Problem #16: Enter your answer symbolically, as in these examples Save
1(a) Given that f(x,y) = 6x²y3 – cosx + 5y - siny + 10x, establish the fact that, the order in which the mixed partials derivatives are taken is immaterial. AN [2] = (b) (i)Find the continuous function whose Laplace Transform is 3 F(p) AP [7] P(p2+4) (ii) Determine [-*[0-3]2+26] AP [2] (P-3)2 +16 (c) Find the solution of the IVP; 2y" - y' – 3y = 4x+ex y(0)=-1. y'(0) = -2 AN [9]
a) Given the following equations: 5x + y = 16 2x + y = 7 Set up the equations in matrix algebra form. Solve for x and y by premultiplying both sides of the equation by the inverse of the square matrix, (using the rules for computing the inverse of a 2 x 2 matrix given in class). b) Given the following equations: 5x + 2y = 9 10x + 4y = 18 Attempt to solve...
3. Defining on (0,2) by 2 ~ y iff sin x = siny gives an equivalence relation. Find [0],[ 72], 3/2), and then find (2), where : #0,7/2, or 3/2.
5x cos(y3)dA Where D is the region bounded by y = 2, y = -x and the y axis.
Solve the following linear programming problem. Maximize: z=5x+4y Subject to: 6x-y≤16 3x+y≥12 x≥2 y≤8 The maxiumum value of 5x+4y is ____ at the point _____ (Type an integer or a simplified fraction.)
QUESTION 16 1 points Save Answer The propagation of uncertainty formula for the equation y-mx b is V(Aym)2+(Ay(Ayb) where Yn-(mx + b) _ ((m + &n)x + b). Дух-(mx + b) _ (m(x + 5x) + b) and 5x and Sb are the uncertainties on m. x and b respectively. Ifm-o/- 0.3. x - -4.8-0.5 and b - 16/-0g then what is the uncertainty on y? O-(mx + b) _ (mx + (b + Sb)). The values 5m, QUESTION 17...
question 2 1. Interchange the order of integration and evaluate the integral S" S" Siny dy dx. 2. Use Lagrange multipliers to find the points on the curve x'y = 16 nearest the origin. 2 Eindholm of
Find the derivative of the function. y sin-1(5x+ 1) Part 1 of 3 The function y - sin-1(5x + 1) is a composition, and so we must use the Chain Rule, given below, to find the derivative dx[f(g(x))) = f '(g(x))g'(x) For the given function sin 1(5x+ 1), the "inside" function is Sx + and the foutside" function is arcsin (a) Part 2 of 3 Recall that the derivative of y sin-1(x) is 1-(5x - 1)2 Find the derivative of...
verify the following 1) tan x+cot y= sin(x+y)/cos x sin y 2) tan 5x + cot 5x = 2 csc 10x