f (x) — х3 — 3х — 4

Q: Co. If FCx)=3x-4,+4+1,finelf(xland f"(x)

A: To find out f'(x) and f"(x).

Q: f= (2xy+ 3x²)ē+ (x² – 2yz + 2y)ē, – (e² + y²)ēz

A: Given

Q: f(x, y) = x4 + 13x³y³ - 5xy4 + 14

A: Given: fx, y=x4+13x3y3-5xy4+14To Find: To determine ∂f∂x and ∂f∂y.

Q: (D³ – 4D²D'+ 5DD² – 2D ) z = e'*2* + Vy +x.

A:

Q: (f) 2x2 + 2r + 11 dr. J (2x + 3)(x² + 4)'

A:

Q: f(x, y) = 75 + 8x+5 Find fx, fxy, and fxyx. 8x³ e-8y

A:

Q: f (x, y) = 6xy+ 2x²y + xy².

A:

Q: f'(x) = z - 4r+ 12z + 12 and f(0) = 7.

A: f'x=x15-4x3+12x+12  &  f0=7 Integrating on both sides with respect to x, we get ∫f'x…

Q: f(x,y)=x² +y° +3xr² – 3y² –8

A: Given f(x,y)=x3+y3+3x2-3y2-8To find critical points, we first compute∂f∂x and ∂f∂y  ,…

Q: y= (2xy+ 3x²)ē+ (x² – 2yz + 2y)e, – (e² + y²)ē

A:

Q: Q2. (a) dy = (x + y + 3)² (b) 2xy4 = 4x² + 3y?

A: Given that a)dydx=x+y+32 b)2xydydx=4x2+3y2

Q: e* y" – 2y' + y =1+x² + 3e*|

A:

Q: 3.2 find fxxy: flxiy) Bx*t 2€y?+ qxy!

A: when differentiate with x then y should be constant and when differentiate with y then x should be…

Q: Solve for x: Ax + By = Cx + D.

A: Solve for x:  Ax+By=Cx+D.   Subtract Cx on both sides. -Cx+Ax+By=-Cx+Cx+D-C+Ax+By=D

Q: Find d²y/dx² for the following equatio: f) x2/3 + y2/3 = 1 g) x³ + y4 = 16

A:

Q: f(x, y) = 8x3 6x2y3 + 7y4 -

A: Given data:     The given function is: f(x,y)=8x3-6x2y3+7y4.   The expression for the partial…

Q: f(x, y) = 2y – 6ry - x 2.

A:

Q: ZZ= X+y O x² +y² x² - y O

A: The given expression is zz. Let z=x+iy. Then, z=x-iy.

Q: 8. (D2- 2D+ 1)y = xlnx

A:

Q: y"'-3y"+2y'=t+et

A:

Q: Not sure how to start problem

A: Given functions are We find g(f(x)) by replacing x by f(x) in g(x)

Q: Find fxy(-1, 2) if f(x, y) = 3xy2 - 2y + 5x?y2 O 40 О 34 О-32 -28

A: Let's find.

Q: f(x,y)=(3x^2+3y^2)

A: Given, f(x, y)=3x2+3y2 BOUNDARY OF A DOMAIN :- It is the set of all boundary points of the domain D.

Q: Q.2 a- If w=xy+ find y2 +1 a²w a²w and дхду дудх

A: Solution Part A  Given. w = xy+eyy2+1  We have to find ∂2w∂x∂y   and  ∂2w∂y∂x

Q: F(t) = VN + Nt2 %3D

A: Given that F(t)=15+15t2 The fourier series will be f(x)=a02+∑n=1∞ancosnπx/L+bnsinnπx/LWhere…

Q: (s-2) F(s) = [+ %3D (s-2)2 + 16

A:

Q: 2r2-12r+18=o 2x+12x+21=O 2. yL+2x-Y=D

A:

Q: E. Find x²+y = 4 %3D

A: x2+y2=4

Q: d. xy' – y – 5x* – 3x² + 2x = 0 when x = 1 and y = 2 -

A: first write teh differnetia; equation in standard form and then solve.

Q: f(x, y) = x³ – 2ry + 27y³.

A: Given: f(x,y)=x3-2xy+27y3 To find: Local extrema and saddle point of the function.

Q: y = vx – 3(x² – 1)

A: The product rule of differentiation states that uv'=u'v+v'u.

Q: (j) z = y² – x² + 2x - (k) x² – y² + z² + 4.x + 2y = 3

A:

Q: f(x, y) = 6x - 2x' +3y +6xy

A: For critical points, ∂f∂x=0∂f∂y=0

Q: r. = x (n) |1,

A:

Q: Qs) y" + 3y' + 2y = e* – 3

A: See the details solution in below

Q: y"-2y'+y = e* Inxr

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

Q: f R(x) = 4x and C(x) = 0.004x + 1.5x + 50,

A:

Q: y = In(x² + 4)

A:

Q: y" – 3y + 2y = x-1 (using the method of undetermined coefficients]

A:

Q: t3 - 1-2vt f(t) 3D -t5

A: on doing differentiation with respect to t we will get

Q: 2xyy' + (x – 1)y² = x²e* |

A: We need to find the general solution of the given differential equation 2xyy'+(x-1)y2=x2ex The…

Q: x²y" – 3xy' + 4y = 0 Answer y(x) = (c1 + c2 In x)x²

A:

Q: (D² - 2D+1)y=(2+x²)e* .

A:

Q: y" - 6y' +9y = e", 3x У (0) -1. у(0) -0

A:

Q: x2 + 4y2 + 322 = 3 дх ay

A:

Q: d. xy' – y – 5xª – 3x² + 2x = 0 when x = 1 and y = 2 -

A: It is the linear equation of first order.

Q: Мaximize Z = 14x + 21y subject to 2x +3y 0

A: This is the simple problem based on linear programming problems (multiple optimum) which could be…

Q: Use Cramer's Rule to solve the system.

A:

Q: 17) Find DE 3r- 28 3x- 30 D F 33

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

Q: de J( - 2)V- 4x + 3

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.