If 8(x)=7cos 9x, in T13) then suggested form of y(x) is: [A] 7sin Ar+7cos Br [B] Asim 9x. [C] Asin 9x+Bcos 9x. ID] Bcos 9x [E]none. 2jf g(x) = 7e", in 773) and y e " + exe". G. ER in T1). then final form of y,(x) is: (AJA [B]Are [C]Are [D]Ac" + Hre" [E]none. 3)The general solution of y"+ 4y = 12, is: [4][ya = sin 2x+c, cos2x+12,6%, ER] [B][yo = sin 2x+c.cos2x+3,4,,ER] C%=+ce +3,9,6, ER] [D).=+ce* +34,6,,C,ER] Enone,
3. Suppose f(x,y,2)-sin2(x)-2sin(x) + y. 4 y z + 52.62. Find the minimum value of this function. you must find the point at which the minimum occurs and "prove" that the function really has a mini mum there. Does the function have a maximum? If we restrict the variables to the ball of radius 1, centered at the origin, does the function have a maximum on that set? (You don't have to try to find the maximum but you should...
(1 point) Find y as a function of x if y" – 7y" + 10y' = 12et, y(0) = 10, y(0) = 29, y' (0) = 10. y(x) = (21/2)+(41/2)^(2x)-3e^(5x)+3e^(x) 000 (1 point) Find a particular solution to y" + 36y = –24 sin(6t). yp = 16-3e^(-3t)-8cos(3t)
At the indicated point for the function, find the following. (Round your answers to the nearest whole number.) y = (x3 + 2x)3 at x = 2 (a) Find the slope of the tangent line at the given value. (b) Find the instantaneous rate of change of the function at the given value.
Find the first partial derivatives of the function. f(x, y) = 2x + 4y + 8 fy 2 fy = 2 X
(1 point) Find y as a function of x if (0)- 3, y' (0)-8, y"00. y(x) -
8-9r 7-8x (1 point) Find the inverse function to y = (x) = . x=f-1(y) = help (formulas)
Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.) y = 2x - In x (x, y) = _______ Describe the concavity. (Enter your answers using interval notation. If an answer does not exist, enter DNE. concave upward concave downward
Find all y-intercepts and x-intercepts of the graph of the function. f(x) = 2x² – 2x² – 32x+32 If there is more than one answer, separate them with commas. Click on "None" if applicable. None ajo y y-intercept(s): 1 DO X $ ? x-intercept(s): 2
(1 point) Find the solution of 4x2 y" + 2x²y + y = 0, x > 0 of the form yı = x” (1 + (1x + c2x2 + c3x3 + ...) Enter r = Ci = C2 = C3 =