dA, R = {(x, y) : 0 < y< 1,0 < x < 2VI} xe

Q: fo axy dx + 2xy dy, where Cis the rectangle bounded by x = -1.x = 1, y = 1, and y = 5. 6xy dx + 2xy…

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Q: I=Jx Incx) dx, where b is a constant with %3D bフ)

A: Intregation of product of two variables is given below

Q: H.W: O Selve the sec X :Ans, y-c Cosk +Casnx+Xsinx-

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Q: Folve the integration J= (x cos 2x dx, 8

A: In the given question, the concept of integration is applied. Integration Integration is a method of…

Q: M-2-Sin(X y) nd dm dt X = t. yclint Z=et-1

A: Differentiation

Q: At what points (x, y, z) in space are the functions in continuous? h(x, y, z) = ln (z - x2 - y2 - 1)

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Q: dy If x = t - t3 and y = t2 - t, the value of at t = 2 is %3D %3D dx

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Q: lim r.y)→(0,0) (4 + (x² + y²) In(x² + y?)) Dose not exist -00 00 1 4-

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Q: dy at x = 2 for the function below. Evaluate %3D dx y = - 8u + 8u + 2, where u = 3x2 – 7x + 9

A: Note: As per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: The temperature at a point (x,y,z) is given by T(x,y,z) = 1300e^(-x^2-2y^2-z^2) where T is measured…

A: given that T(x,y,z)=1300e(-x^2-2y^2-z^2) . we need to find the rate of change of the temperature at…

Q: dy at x = 2 for the function below. dx Evaluate у%3D — 2и + 4и + 9, where u %3D 4x2 — бх + 5

A: Given that,    y=-2u3+4u+9, where u=4x2-6x+5

Q: f (x, y, 2) = In (x² + y? + ²) ve df x = cost, y = sint, z = tise dt It%=D1

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Q: Let v(x, y) = cos(4x)sinh(4y). Find f(z)with Im(f(z)) = v(x, y). I

A: Given function is v(x,y)

Q: TEANUCOGl b) Given z = f (x – y, 2x – 2y, 3x – 3y). Show that - dz dz = 0. he

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Q: af Find of f (x, y) = sin %3D dx 1+ Y COS 1+y () Option 1 sin 1+ y 1+ y Ontion 4

A: Partial derivative of a function in several variables with respect to one variable is calculated by…

Q: dy Assuming 2x -8y2 + 10xy = 0 defines y as a differentiable function of x, use the theorem Fx to…

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Q: dy +y de : 2 et dx Arowar 1- ye" (c -x*) 1= yet (c -x*) %3D

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Q: valuate S S Se(3 – 4x)dV, whe e xy-plane defined by 0 < x s

A: To find: ∫∫∫E(3-4x) dV

Q: (* +y – 4z) dV where E = {(x, y, z) | 0 < y < 2, 0 < * < y, 0 < z < a +y?} Evaluate

A: ∫y=00∫x=0y∫z=0x+y2x+y-4z dz dx dy Now, ∫z=0x+y2x+y-4z dz =x+yz-2z2z=0x+y2 =x+yx+y2-2x+y22…

Q: f(x, y, z, w) = (1+x+ sin(z − 2y), ez-w, 2z+tan(w+x²)).

A: we have to find the approximation of ƒ at the point P = (0, 0, 0, 0).  For this we use the proper…

Q: Find fa, fy, and fz. f (x, y, z) = 3z In (x°y³ cos(4z)) fr = %3D fy = fz =

A: Given that , fx,y,z=3zlnx6y3cos4z find fx , fy and fz.

Q: Let r(t) = (cost,sin t, ln(cost)).Find T, N, and B at (1, 0, 0).

A: Let rt=cos t, sin t, lncos t at 1,0,0 Find T, N and B. Tangent vector to the curve is denoted by…

Q: valuate F. dr, where F(x,y) = xyi + 3xyj, and C is given by r(t) = 3ti + 2tj, 0 <t <1. C %3D nter…

A: first, we will substitute the value of x, y, and z from r(t)=3ti+2tj in F(x,y) where 0≤t≤1 we get…

Q: r(x, y) = ln(x + y) w = x sin(y) + y sin(x) + xy

A: In partial derivative, while taking the derivative with respect to one variable consider other…

Q: At what points (x, y) in the plane are the functions continuous? ƒ(x, y) = ln (x2 + y2)

A: To find the points in the plane

Q: 31. f(x, y) = e cos y a. (0, 0), b. (0, п/2) %3D at

A: We know that linearization of f(x,y) at (a,b) is

Q: fze [sin(3x)]-m(x, y, z), where m(x, y, z) = Part C. yz-1 %3D

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Q: alculate the double integral. tan e dA, R= {(x, y). 10<0S7/3, 0<tS 1/2.}

A: Given the double integral

Q: dz Given z = e* sin y,x u? + v2,y = uv, find - dv %3D %3D

A: Here I am attaching image so that you understand each and every step.

Q: The degree of the homogeneous function f(r.y) = sin--tan- is Enter your math answer

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Q: Find the differential dy. (a) y = xv8- x %3D dy %3D (b) y = (1+ x)7 dy

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Q: y = x* + 1, y = 0, x = 1 around the ar axis.

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

Q: f(x, y) = 2x- xy + y, find (a.)and (b.) at (Xo, yo) didirectly from the definition. dx dy

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Q: f x = sec(z) and y = tan(z) , then dy at z = dx 4

A: We can use the chain rule of derivative in order to solve the given problem.

Q: Y" - Y = { 2, %3D Ost Y(0) = Y'(0) = 0, %3D %3D t21

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Q: Evaluate : || x sin(y) – y sin(r) dA where R= {(r, y) | 0< # < n/2, 0 < y < a/3}.

A: It is given that double integral is ∬xsiny-ysinxdA where R=x,y0≤x≤π2,0≤y≤π3. It is known that double…

Q: xy cos y dA, R: -1 <xs 1, 0s ys

A: Given: I=∬xycosydA And R: -1≤x≤1 , 0≤y≤π As we know that: The expression for the integration by…

Q: f(x, y) =- sin xcos y, then

A: The given function is: f(x,y)=-sin xcos y To find ∂2f∂x2. Here, note that y is constant w.r.t. x.

Q: f z = f (x, y), where x = r cos 0 and y = r sin 0, show that a2 z 1 a²z 1 dz ar2 ar2 p2 aA2 r ar

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Q: find the dy リ=(メ+z)mx, (xを when 3In X

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Q: Find the I.F of y(2x-y+1)dx+x(3x-4y+3)dy=0.

A: Given equation is y2x-y+1dx+x(3x-4y+3)dy=0

Q: E). f(x, y) = sen?(r2 – 0²) + In(r0 + 0), r = Vx2 + y² 0 = arctan con -

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Q: h(r, y) = h(0,0) = 0 3x2 + y2 (i) Prove that |h(r, y)| <ly

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Q: y' = x+y+xy, y(0) = 1 at the point x = 0.1 (h=0.02) Use 4th order RK

A: Given y'=x+y+xy where y=1 when x=0. The objective is to find y0.1 using Runge-Kutta 4th order…

Q: sin(r. r dr dy. Compute O y/3

A: To evaluate∫01∫y131sin(πx2)x2 dx dyx= y13y = x3

Q: dy Assuming - 9x³ - 2y - 7xy = 0 defines y as a differentiable function of x, use the theorem Fx to…

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Q: y sin (r²) dt

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Q: (a) Show that y = x* is concave upwards at the origin and y= e* is everywhere concave upwards.

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Q: The longest interval in which the I.V.P y" + (tanx)y-xy x, y(1) = 3, y'(1) = 0 surlay has a solution…

A: Given,  y''+tanx y'-xy=x It is of the form,  y''+p(x) y'+q(x) y=g(x)