Given: f (x, y, 2) = z0 + 5x*y%z® _ #°yA 2x°y" + 5æ*y®z° – z°y4 ,3,,7.5 .48 3.4 Required: fzay, fzzy

Q: Find the value of c > 0 such that the regionbounded by the cubic y = x(x - c)2 and the x-axis on…

A:

Q: 4. Evaluate S, cos dA where D is the region bounded by D = {(x, y)/ VL < x < v3Ln , 0 < y< x² }.

A:

Q: Evaluate p (x² – 2xy)dx + (x²y +3)dy around the boundary of the region defined by y? = 8x and x = 2…

A: To evaluate : ∮x2-2xy dx+x2y+3 dy around the boundary of the region defined by y2=8x and x=2 (a)…

Q: 46.) (a) Parameterize S the 1st octant portion of the cylinder y² + z² = 9, 0 <x<4 (b) Use above to…

A: y2+z2  0≤x≤4x=uy=3 cos vz=3 sin vparameterise the surface ass(u,v)=(u   3 cos v   3 sin v)0≤u≤4,…

Q: 1. Compute  E yz dV , where E is the region above z  0, below z  y, and inside x 2 y 2  4

A: Obtain the limit of integration as follows.

Q: Let f(r, y, z) = In(r2 + 2) + y?e* – cos(2yz). Find Szya- Find all the relative extrema and saddle…

A:

Q: Let f(x, y) = xcosy- y'e*y. fry at (1,0)is equal to: %3D | -2/3 -2 1

A:

Q: a. Determine the temperature u(x,t) in a rod of length L, given the following conditions: aul au =…

A: Given

Q: 11. Given: WX||YZ; XY||ZW Statements Reasons Prove: AWXY = AYZW Y 3. Z. W

A:

Q: 2 Let f (x) = x on [0, 1] Calculate x dx and x dx by dissecting O, I] oaual narts and hence show…

A: Given

Q: az əz 1. ax' dy If z = In(e* + e"), show that %3D %3D

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

Q: 5. Evaluate Fale JJJ (²+ + ² dv, where a, b, c > 0, and & is the region given by E 22 + y² 2² 6² +2…

A: Given triple integral is ∫∫∫Ex2a2+y2b2+z2c22dVa,b,c&gt;0x2a2+y2b2+z2c2≤1 in the first octant. Now,…

Q: In(u cos v) and y = usin v. Evaluate and z at the point 2е" In y, x 3D (u, v) = (2, 7/4). Let z = du…

A:

Q: pプ PG2-2(6x)さ子エ theorem over the elosed hemispher defined bY Zz J25-x²_y?

A: Given that F→=x2+yi^-zyj^+z2k^ and z=25-x2-y2

Q: The area bounded by the curve y3a and the lines z 4 and a-9 above the z-azis is aquare units O 27v0…

A:

Q: 9. Use Green's Theorem to evaluate (e* +y²) dx +(e" +x²) dy where C is the boundary of the region…

A:

Q: Under a change of variables z = u°/3, y = v²/2 , the infinitesimal element of area dædy becomes 6uv…

A:

Q: Let ry w = and a = 2s + t, y = st, z = 2s - t dw dw Find ds' at

A:

Q: a) Evaluate ff, (3 – 4x)dV where E is the region below z = 4 – xy and above the region in xy – plane…

A: To evaluate the given triple integral.

Q: 6. Given: AUVW = AXYZ Prove: UV || XY .Y W

A:

Q: find the indicated extrema, assuming that x, y, and z ar = xyz z - 12 = 0

A:

Q: For z + y, lim ()(1,1) Va - A. 0 В. 2 C.1 D. Does not exist.

A: This is simple question can be solve by rationalising the given function Solution is given below

Q: 2. In A ABC, X is the centroid. A A If CW = 15, find cx and XW. W, B. If BX = 8, find BY and XY.

A: we know that  centroid is located 23 of the distance from the vertex along the segment that connects…

Q: Let f(x, y) = xcosy-y e*y. fry at (1,0)is equal to: %3D 1

A:

Q: Let H(x) be an antiderivative of 1sm z if H(5) = 7, then H(2) =

A:

Q: f (x, y) = xlx - alny is %3D O homogeneous 0 degree O not homogeneous O homogeneous 2nd degree O…

A:

Q: Given w = In(") + 8z*y* /z find %3D mmadı zerinden mmis xy + 12.x ayu Ob. 72x y 12E +96x'y Od.…

A:

Q: The auxiliary (charasteristic) equation of the DE x²y" + xy' + y = 0 is %3D

A: Euler-Cauchy type differential equation: Let a equation x2y''+y=0 ..(i) Put y=xm in the given…

Q: in the Figure chown below, x i a cmls while y is decreasing at 3 cmls.Calculate z is changing X =…

A: Let's find.

Q: MLx,y) dx +x(x,g) dy. 1 chek the Coudi'tied deu Jy dx ® intey.coke MWirit X reyarding y as coustunt.…

A: SOLUTION

Q: 4. Evaluate fl, cos (2) dA where D is the region bounded by D = {(x, y)/ vLT <x < V3Ln,0 <y< x² }.

A:

Q: (x, y, z) = VI - xVE – y. (x, y) In(1-x) In(z+y). (х, у). (x, y) = D. (x, y) = VT – x + y². /1 - x +…

A:

Q: Evample: y-xy, Yu)=1 and h:o.l a pproximale Y(1 3) using improved Euler Muthocd.

A:

Q: Let f(x,y,z) = zIn(x³ycos(z)), find Z 3x² O In(x3ycos(z)) - ztan(z) 0 2 Y о 3z X af ila

A:

Q: 10- Evaluate JJI where E is the region that lies inside the cylinder Vx2 + y?dV E x? + y? = = 16 and…

A: Here we use polar coordinate and Jacobian .

Q: Consider the S.mpto lincar rogressic 3:0n m adol Y tX; t U ukon exp(az.) You have the fallow. ng…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: : 0s 0s n, Os zs 1, 6Vzs rs 6}. Let E= Compute y?e(x2+y?)³ dv•

A: Given that, Let E=r,θ,z : 0≤θ≤π, 0≤z≤1, 6z≤r≤6 compute ∬∫Ey2ex2+y22dV

Q: Evaluate 7x dV where E is the region that lies inside the cylinder x2 + y² = 8 E and between the…

A:

Q: 5. Evaluate z dV, where E is bounded by the cylinder y? + z2 = 9 and the planes x = 0, y = 3x, and z…

A:

Q: Let f(x, y) = xcosy-y e*y. fry at (1,0)is equal to:

A:

Q: 10 The double integral 2x dædy, where T is the triangle with vertices (0,0), (3,0) and (6,3), equals

A:

Q: 16. WXYZ is an isosceles trapezold with WX ZY If mĐW = (2x)° and mĐZ = (x +27)°, find the value of…

A: We have to find x

Q: 3: The volume Vof water in a spherical tank of radius R is related to the depth h of the water by:…

A: As per the guidelines I'm able to give you only one answer because this question is not a…

Q: dz for z = da z In(zy) + y, y = c os (x² + 1)

A:

Q: 3 Find the bounded Solution of : = xt メ>。,t>。 >y(メノ) where y cx, o) = %3D and y co,t) = 0 . Ansi] y=…

A:

Q: What is the additional condition for a cubic-spline S(x) that passes through n data points (x1, Y1),…

A:

Q: Use Green's Theorem to evaluate (e" + y²) dx+ (e" +x²) dy where C is the boundary of the region…

A: we have to evaluate the following by using greens theorem

Q: If f(0)=f(2), find the sum 2c+d for the following cubic spline S(x) with clamped boundary…

A: The clamped boundary conditions in this case can be defined as follows.

Q: Find the Sof (x, y,z)dV A. Q = {(x, y, z)|(x+y² +z 4 and z = x+y, f(x,y2) = x+y} B. Q= {(x, y, z) (x…

A: We will use the basic knowledge of integral calculus to answer this question correctly and…