3x3+y² x²+y² .2 (x, y) ± (0; 0), ,2 ) f (x, y) = 1, (x, y) = (0; 0).

Q: xyz 3. If (x, y.2)= In +ef), find f,,f, and f.. 4

A: Given: fx,y,z=lnxyz4+e-3xy2z2 The objective is to find fx, fy and fz

Q: -16 1Δίνεται η συνάρτηση f)- 2x+8x i) Ποιο είναι το πεδίο ορισμού της f i) Να απλοποιήσετε τον τύπο…

A:

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = 1 + xy2 - 2z2

A:

Q: X - X (r-F (x-X\r-F) X (x –x) |Y Y-Y 2 1 4 3 4 Compute: X = %3D %3D E(X- X(Y -Y) _ %3D N- 1 B = 2.…

A: x x-x (x-x)2 y y-y (y-y)2 (x-x)(y-y) 0 -2 4 2 -2 4 4 1 -1 1 2 -2 4 2 2 0 0 4 0 0 0 3 1 1 6 2…

Q: (2xy+ 3x2)e, +(x² – 2yz + 2y)e,- (e2 + y?)e, olan f(x, y, z)

A: Given that the function is

Q: X1, X2 2 0 12. Minimise Z = 60x1 + 80x2 bo Subject to 20x +30x2 2 900 40x1 +30x2 2 1,200 X1, X220 LO…

A:

Q: y''-3y'+2y=5e^3x,y1=e^x

A: Reduction of order is a very significant and basic method to solve higher-order linear differential…

Q: f(x, y) = 1 + x2 - y2 R = {(x, y): x2 + y2 < 1}

A: Find the area of surface given by z= f(x,y) that lies above the region R.

Q: 8. Find the general solution of (x2 + y2 + 1) dx + (x2 – 2xy) dy = А. х2 - у? - ху — 1%3D Сх В. х2 +…

A:

Q: r/64–x² r61-x²-y² x dz dy dx -67+x²+y²

A:

Q: Obtain the particular solution of (3x2 - 2y2)y' = 2xy; x =0, y=-1.

A: We have to solve

Q: 6 - 3x2 + 3 Find the general antiderivative of f(x) - - - x5 + C

A:

Q: 3 '9-x2 3+V9-a2-y? 1 dz dy x² + y² x²+y² a C = L7I Fle,0,6) dp dộ do

A:

Q: 4) f(x, y,z) = /1– x² – y² – z²

A: Domain is the subset of R3 where the function is defined

Q: find dy/dx

A: Known formula: ddx∫rxqxftdt=fqx q'x-frx r'x.

Q: (2xy + 3x²)e, + (x² – 2yz + 2y)e,- (e2 +y²)e, olan f(x,y,z)

A:

Q: 2. T1: R2 - R2, T1(x, y) = (x – 2y, 5x + 2y) T2: R2 - R2, T2(x, y) = (0, x)

A:

Q: x- + Y- (e) Ā = (e) Ã = + C : {y = 0, z = 0, x € (0, 0)} x² + y²' t ey x² + y2' C: {x = 0, z = 0, y…

A:

Q: Зх — 4у + 23 (a) f(x, y, z) = '9 – x² – y² –. - V2t – 4 x² – y? - (b) g(x, y, t) : -

A:

Q: 2. y" – 2y' – 3y = e²", y(0) = 1, y (0) = 0, Yp(t) = -e2' /3 %3D

A:

Q: f (x, y, z) ) = x² + y² + z²; x* + y* + z* = 1 2. 4 || ||

A:

Q: x" + 2x' + 8x = 2e-2t - e-t,x(0) = 1, x'(0) = 0

A: Given differential equation, x''+2x'+8x=2e-2t-e-t,x(0)=1,x'(0)=0 The objective is to solve the…

Q: x² + y² = (3x² + 2y² – x)², (cardioid) 0, y 0.5 -0.5 0.5 1 -0.5

A: Giv:    x2 + y2 = ( 3x2 + 2y2 x )2     Point: ( 0 , 1/2 )

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

A:

Q: y = x(arctan x)² arctan (x+ (1+x²)arctan x) А. 1+x2 arctan (2x+ (1–x²)arctan x) В. 1-x2 arctan (2x+…

A:

Q: In the function given. Evaluate the integrals.

A: Given:∫03 fx dx=2,∫36 fx dx=-5∫36 gx dx=1∫36 3 fx -gx dx=?

Q: .2 f(x, y, z) = 4xy – 8xyz + 7yz² f,(x. y, z) = &xy– 8yz fy(x, y, z) = | 4x- - 8x2 f.(x, y, z) =…

A: To find the first partial derivatives of: f(x,y,z)=4x2y-8xyz+7yz2

Q: How would you interpret the coefficient of β2 in each model? Ln(Y) = β0 + β1 Ln(X1) + β2 Ln(X2) +…

A: Note : Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the…

Q: 16. Using integration by parts to solve 2√4x²+k A. -√4-x² + k √4x²+k -2√4x²+k B. C. x³ dx √4-x² and…

A: Given: ∫x3dx4-x2

Q: X - X (x -x* Y (r-F)} (x-X{r-F) Y-F 2 4 3 6. 6. Compute: X = Y = E(X-XXY-Y)- N-1 B A = Y - B*X = 2.…

A: The table is given as follows x (x-xbar) (x-xbar)^2 y (y-ybar) (y-ybar)^2 (x-xbar)*(y-ybar) 0…

Q: V1-x² 1-x²-y² e-3(x²+y²+z²)² dz dydx a) Evaluate

A:

Q: 2d) Let a e R find the solution of y' (x) – ay(x) = 0

A: as you didn't mention question number to be solvedso I solved first question. For Further solution…

Q: 22) Find all critical points? f(x,y)=4xy+x4+y4

A:

Q: 2x + y + z = 1 X- y+4z = In1 x + 2y - 2z = 3

A: We will solve this equation with the substitution method. So first of all we will find anyone…

Q: f(x, y, z) = V9 - x² – y2 – z²

A: The given problem is to find the surface for the given function of three variables. Given function…

Q: y fa(4y) -1.0 -2 1/8 -0.5 -1 1/4 1/2 1/8 0.5 1 1.0 2 Find the E (X), E(Y), V (X), and V (Y). 2.

A:

Q: px + qy=z-a √x² + y² + z²

A:

Q: ze² dz (1+ x)* + C 1+ z

A:

Q: 6) Find most general antiderivative of the fxn. a) f(6) = x5+2x²-1 X' B) 4(1) - 2 +30*

A:

Q: 1.y' + 6t = e*t, y(0) = 2 2.y" + 6y' + 4y = 0, y(0) = 1, y' (0) = 0 3.y' +t = e5t, y(0) = 1

A:

Q: (2xy + 3x²)e +(x² – 2yz + 2y)e,y- (e² + y²)e, olan f(x, y,z)

A: Given

Q: 48xyz < (3x + 2y)(y+ z)(3x + 2z) for every x, y, z E [0, +∞[.

A:

Q: 3 9-r22 1 dy dz dr 9-r2 0_æ²_22 (x² + y² + z²)1/2

A:

Q: Find all the local maxima, local minima, and saddle points of the functions in Exercises 11-20.

A: (10)Consider the provided function, fx,y=x2+2xy Find all the local maxima, local minima, and saddle…

Q: 2X + y - x - 2y + 2z = -11 3x - y + z = (x, y, z) =

A:

Q: 6. Differentiate y with respect to x using A-method. x-3 a. y = X b. у %3D V4x + 3

A:

Q: 4 | V1+y dy 3 ((1+9) GAC). ZV 2). 3 for KQuestion 6.6.13 -1/2 -x S= 27 V1- a21+ dx -1/2 r1/2 dx =…

A:

Q: Distanced is given by the distance formula.

A: Given points are P1x1,y1 and P2x2,y2. The distance between P1 and P2 is "d".

Q: x - 1 = λχ y = 2 = λy z = -λz (x² + y² = z² = 0,

A:

Q: (b) f(z)= (4 – 5e*)³ x² + 1 (c) f(r)= ez %3D (d) f(z) = e=²–5z+4 ez-5x+4 (e) f(x)=xe² – e² = re² –…

A: We can solve this as follows:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.