show all working please 10 Given z = 2 – j2 is a root of 2z' - 9z2 + 202 - 8 = 0 find the remaining roots of the equation. Find the real and imaginary parts of z when 1 2 1 2 2 + j3 3 - 2 .. Find z = Z4 + z2z3/(z2+z3) when 2, = 2 +j3, z2 = 3 + j4 and 23 = -5+j12. Find the values of the real numbers x and...
7a please SM 7. Consider the problem min x? - 2x + 1 + y2 - 2y s.t. (x + y) x +y + b = 2/a where a and b are positive constants and x and y are positive. (a) Suppose that (x, y) solves the problem. Show that x and y must then satisfy the equations x = y and 2r'+br = a The equations in () define x and y as differentiable functions of a and b....
1. Given that y, - e is a solution of (2x-x') y" +(x-2) y'+2(1-x) y. a. Find the general solution on the interval (2, o). y(3)-1 b. Find a solution of the DE satisfying ¡y(3):0 1. Given that y, - e is a solution of (2x-x') y" +(x-2) y'+2(1-x) y. a. Find the general solution on the interval (2, o). y(3)-1 b. Find a solution of the DE satisfying ¡y(3):0
2. Sketch the graph of the following functions and find the values of x for which lim f(x) does not exist. b)/(x) = 1, x = 0 f(x)- 5, x=3 c) x2 x>1 2x, x> 3 d) f(x)-v e) (x)- [2x 1- sin x Discuss the continuity of the functions given in problem #2 above. Also, determine (using the limit concept) if the discontinuities of these functions are removable or nonremovable 3. Find the value of the constant k (using...
Please show all work 1. Find the area of the region bounded by the graphs of the given functions on the intervals indicated. a. y = x2 + 2, y = x, (2,5) b. y = (2x +1, y = 3x + 2, [0,2] C. y = ex-1, y = x,[1,4]
can you please answer all of them please need it for a review F(x y, z) = 6x over the rectangular solid in the first octant bounded by the coordinate planes and the planes X-9, y-3, 2-S 27 1458 162 243 Find the center of mass of a thin triangular plate bounded by the coordinate axes and the line x + y = 4 if o(x, y) = x + y. 5 5 -3.73 . Oz Find the center of...
1. Ssinhx – cosh xd sinh x - cosh x 2 coth'(x) + 1 coth2(X) - 1 dx 3. S cosh² x dx 4. S sinhᵒ x dx ctanhx- sinh x sinh 2x
3x+2 f(x) =( :) (x-> +1) Your problem: using the rules of differentiation, find the derivatives of the collowing: f)-(3442) fool(3x+2) (-5x + x + 1) - 2 1 =(-15x 10x" + (-2x = 2) =>15x410x5 - 2x = = 3x -3x- 27 (X)(3+0)-(3x+2)(1) x² g'=(x) =F12x15x4_2 = -5x6 xb * please check my work, if wrong, please write out correct solation! Chain Rule: When functions are composed, to take the derivative involves both the outside function and the inside...
please answer all the following quesitons and show all working 1. Find the general solution to the following homogeneous differential equations. y" - 2y' + y = 0 (b) 9y" + 6y' + y = 0 4y' +12y +9y=0 (d) y" - 6y' +9y = 0
2. (a) Use L'Hôpital's rule to calculate him 2 cosh(2 – 1) – 22 + 2x 3 (x - 1)4 (b) Find the Taylor polynomial P4(2) of f(0) = cos(- 1) about x = 1. (C) Now use P4(2) to check your limit calculation from part (a).