1. Find the antiderivative for each function when C equals 0. Check your answers by differentiation (c) (a) g(x) -5x-6 (b) Һ(х) %— х - 6 k(x)x6+3x2+4 (a) G(x) (b) Н(х) %3D (с) К(x) 3D

Q: b3 (a 0, b 0) is y The critical point of the function f(x,y)=Dxy+

A: Here we use differentiation with respect to x and y of the function  f(x,y)=xy+a3x+b3y

Q: 5. Test the exactness of ODE, if not, use an integrating factor to make exact and then find general…

A: Differential equations

Q: (b) Use the method of complementary functions and particular solutions, to determine the general…

A:

Q: 28. Find the critical points of f(x) = x3 – 3x2 - 3. а. (0,—3)аnd (2, -7) b. (0,3)and( 2,7) c. (0,2…

A:

Q: 1 (a) Evaluate the integration of the following functions: x 2 +2 (i) (ii) fx*e*. dx

A:

Q: 9. Find the most general antiderivative of the function a) f(x)=12+ sin x b) f(x)= 3x(x-5)

A: see below the answer

Q: Solve: x"-x+ 5 y'=t y" - 4 y-2x' = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

A:

Q: 4.1. Estimate f(3). 4.2. Estimatef'(3). 4.3. Give an equation for the tangent line to y = f(x) at x…

A: To estimate f(3), find the value of y when x=3 from the given graph When x=3, the value of y is 3.5…

Q: 4 solve the D.E " -X² Joly =0 3x2 ydx + LY

A:

Q: Find the value of x for which the marginal profit is zero. C(x) = 2x, R(x) = 6x - 1,000 О а. х33,000…

A:

Q: If a quantity grows/decays at a rate proportional to its size, its growth can be expressed as dQ/dt…

A:

Q: Consider a competitive market in which price adjusts to excess demand or supply and firms enter and…

A: dpdt=0.5(qD-qS)qD=30-2p  and qS=2Ndpdt=0.530-2p-2N=15-p-3N   ...(i)dNdt=54(p-10)…

Q: f(x, y) = log, (3x) fe dy In(3x)/(yln(y)2)^2 ||

A: Topic- partial differential

Q: D. Fina the total differential of the function xye¬(x²+y*),

A: Given: f(x,y)=xye-x2+y2

Q: II. Find the particular antiderivative of the function f(x) = e" (2" – 1) whose graph passes through…

A: Given

Q: Use implicit differentiation to find dy dx when x = 1 if x + xy + y2 = x3y2.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Solve the initial value problems for y as a functionof x. (x2 + 4) dy/dx = 3, y(2) = 0

A: Given Data : Differential Equation x2+4dydx=3, y2=0                      1 The given initial value…

Q: Solve the initial value problem for y as a function of x. (x² + 25) dy %3D 29, у(5) %3D 0 dx

A:

Q: Find the general solution for y' = x – 4xy using an integrating factor.

A:

Q: Solve: x" -x+ 5 y'=t y" - 4y-2x = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

A:

Q: x² +y F(x,y)=- x- y - is a homogeneous function of degree

A: Topic= Function Degree =1

Q: 1. e-st cosh t dt 2x +4 2. 2x2 + 21x + 34

A:

Q: 1. Find the relative maxima and minima of y by the second-derivative test: (a) y = --2x? + 8x + 25…

A: Consider the provided question, According to you we have to solve the part (b), (c) and (d). (b)

Q: Solve the initial-value problem for y as a function of x. (16 – 2²) dy 1, y(0) = 7 dæ Y =

A:

Q: (x² + 4) dy 山 3. y(2) = 0

A: we know that ∫dxx2+a2=1atan-1xa+C,  where a>0 see below the answer and calculation

Q: 11) Find the antiderivative: f -3+6√x³ √√x dx

A:

Q: Find the number of units x that produces the minimum average cost per unit C in the given equation.…

A: given

Q: Solve: x" -x+ 5 y'=t y" - 4 y-2x = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

A:

Q: find the general solution of dy/dx + (3/x)y=2/x^2 as a function of x

A: Given,           dydx+3xy=2x2

Q: (d) The GoldPlus Company determines that the marginal cost for their Aiibe 64GB flash drive is given…

A: Given that : Marginal Cost Function is : dCdx=-0.02x+6. We can achieve Total cost function by…

Q: If µ(x) ef (x) is an integrating factor of linear D. E x y' + xf(x) y = x* y – x² sin x where f' (1)…

A: To find - If μx = efx is an integrating factor of linear D.E. x3y' + xfx y = x4y - x2 sinx, where…

Q: 1) In this problem, let * = 2, the value Ar = dx, dy = f ' (x)dx, and Ay = f(x + Ax) - f(x) to…

A: According to the guidelines issued by the company We are supposed to answer only one question.…

Q: 1- Find the average rate of change for y == Xo = 1 X1 = 2 2- Find the instantaneous rare of change…

A: Application of derivatives

Q: Find Solution of the Attached ?

A: Given differential equation is 3xy'-y=lnx+1 and y1=-2. Given differential equation can be written in…

Q: Suppose that the amount of energy (x, y, z) emanating from a source at (0, 0, 0) is inversely…

A: a)  The energy function is proportional to z And, it is inversely proportional to 11+x2+y2    So,…

Q: Solve the initial value problems for x as a functionof t. (t2 + 2t) dx/dt = 2x + 2 (t, x > 0),…

A: t2+2tdxdt=2x+2⇒dx2x+2=dtt2+2t Now integrating on both sides, we get…

Q: Find an integrating factor as a function of z = x ^ 2 + y ^ 2 for the following equation and then…

A:

Q: Let y = 3x². Find the change in y, Ay Ay when x when x = = 5 and Ax = 0.3 Find the differential dy…

A: Given f(x)= 3x2

Q: Find the particular antiderivative of the function f(x) = e"(2" – 1) whose graph passes through the…

A: Integration

Q: 1. Eliminate the arbitrary constants on the given equation: y = A + Be*

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Solve the initial value problems for y as a functionof x. (x2 + 1)2 dy/dx = √x2 + 1, y(0) = 1

A: x2+12dydx=x2+1⇒dydx=x2+1x2+12⇒dydx=1x2+132⇒dy=1x2+132 dx Now integrating on both sides, we get…

Q: x²y" + 3xy = 2 O -y

A: see below the answer option (d) is correct

Q: s(x,y)=ex^2+y^2 How do I find the critical point of this function.

A:

Q: 3. Derive from first principles using partial differentiation the expressions satisfied by the a,…

A:

Q: Find the value of C using the condition

A:

Q: Solve: x" -x+ 5 y'= t y" - 4y - 2 x' = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

A:

Q: Solve: x"-x+ 5 y'=t y"-4 y-2x = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) & L{y(t)}…

A:

Q: Solve (5x2y2 O a. b. 2 ln 3 In a In xy² + 17y²) dx (x+2)³(x²+9) y³ |(x+2)³(x²+9) Y - -1 3 tan-¹() =…

A: Given 5x2y2-xy2+17y2dx-x3y+2x2y+9xy+18ydy=0

Q: Answer all of the following questions. 1.) Find the equation of the line tangent to f(x) = 6 ln(7–…

A: