Differential equations Questions and Answers

Convert the fraction to a decimal 3 4

Find the quotient Do not round 4 1 38 1000

Find the product 23 X 67

Find the intercept s of the follow y 2x 8

to find the Use lagnange multipliens 2 extreme values of f x y y x subject the constraint x y 4

PART I Show that the following solutions are the solutions to the differential equations indicated 1 sin y cos x y sin x cos y 2 y x ex e y y x 3 y n 1 x y 1 x dx dx 4 Arctan y Arctan x dy 1 y dx 1 x 0

2 y x e e x y y x

Approximate 2 x sin x dx by computing the Left and Right sum using the partition 0 6 4 T 3 2 Your answers should be accurate to at least 4 decimal places Left Sum Right Sum You may include a formula as an answer

Find the normal osculating and rectifying planes of R t cos t sin t t at the point x 2

2 1 Points DETAILS Find f a f a h and the diff

For the given functions f and g complete parts a h For parts a d also find the domain f x x 9 g x 9x a Find f g x f g x Simplify your answer

1 point Evaluate in spherical coordinates the triple integral of f p 0 d cos over the region 0 0 2 0 6 1 p 4 integral

3 49 Consider the following LP text Maximize z 3 x 1 2 x 2 3 x 3 subject to begin array c 2 x 1 x 2 x 3 leq 2 11 3 x 1 4 x 2 2 x 3 geq 8 x 1 x 2 x 3 geq 0 end array The optimal simplex tableau at the end of Phase I is Explain why the nonbasic variables and X1 X3 X4 X5 can never assume positive values at the end of Phase II Hence conclude that their columns can be dropped before we start Phase II In essence the removal of these variables reduces the constraint equations of the problem to x 2 meaning that it is not necessary to carry out Phase II in this problem

y 2y 3y 0 y 0 4 y 0 8 y 0 4

point amina occupies the part of the rectangle 0 x 1 0 y 4 and the density at each point is given by the function p x y 7x 5y 5 What is the total mass Where is the center of mass

ng polar coordinates evaluate the integral R sin x y dA where R is the region 16 x y 25