dw -is equal to: dv If w = 5u, then 5w5 v(1 – 20u In v) 5w v(1 – 20w5 In v)

Q: If J_f{x)dx=10 andJ, f{x)dx= 3, then J, f(4 – x)dx=?

A: According to our guidelines we are supposed to do only one question. Kindly repost the other…

Q: Find V. (F x G), if F(x, y, z) = 14.ci + j+ 13yk and G(x, y, z) = xi + yj – zk. V· (F × G) :

A: Vector

Q: = + E (0 < x < L,0 < t <ox) L Ot u (0, t) %3D 0, и(L,t) %3 0, и(х,0) — А, и (т,0) %3D0.

A: Given - ∂2u∂x2 = ∂2u∂t2 + πL∂u∂t , u0, t = 0 , uL, t = 0 , ux, 0 = A , ∂∂tux, 0 = 0 , 0 &lt; x &lt;…

Q: Exy Find dy it y=(t?r1)", x = t?+S %3D

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Q: (a) f(x,y) = (x² + 1)e" (b) g(w, z) = w? + 22 (c) h(x, y, z) = vT² + 3y – xyz²

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Q: Let ƒ(x, y) = ex + ln(x + y). Find the following a. ƒ(1, 0) b. ƒ(2, -1) c. ƒ(0, e) d. ƒ(0, e2)

A: Given function: fx,y=ex+lnx+y a) We have to find ƒ(1, 0) f1,0=e1+ln1+0f1,0=e+ln(1)f1,0=e+0f1,0=e

Q: Find where 1)let . V°g r = l7| -- g(r) = In(r³) s = xi + yj + zk * vo x Vp 2) find = yz + zx2, P =…

A: Gradient and cross product

Q: aw C. If w=f(x,y) and x=r. cose, y=1. sing. Prove that ar 1 (dw r² 20 = fix² + fy²

A: Let's prove.

Q: Find ▽ x (▽xF) if F(x, y, z)=10xy j+ 10ryz k.

A: The value of ▽ x (▽xF) is (10 + 10y)i + 10xj + 0k

Q: for for w= rs ,Y=uV S=uーv, find and Jw

A: Given w=rsr2+s2, r=uv, s=u-2v To find  ∂w∂u and ∂w∂v By chain rule,…

Q: Find Vx M, if M = V + P, where V = (3xy, 5, x'ny) and P = Vt where t = z csc¯(y csch¯ Vx) + y…

A: Let P=∇τ=∂τ∂x, ∂τ∂y, ∂τ∂z Obtain the partial derivatives as follows:…

Q: f = f (x, y) = u? + 3v, y = uv

A:

Q: Q.22.a) S Vx cosvx dx (hint: let u=V) =Vx, et b)S adt et+let

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Q: Let z= I= 2e", and y = 3 ln v. Find in terms of u and v.

A:

Q: H.W.3: For which values of z is w =1/(z – i), defined? For these values obtain u and v and evaluate…

A: Explanation of the answer is as follows

Q: (x+ 1) dx using the substitution of u =x +3. Vx + 3 (c) Evaluate

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Q: dw and ds dw Assume that w = f(s³ +r?) and f'(x) = e*. Find dw dw ds II

A: Partial derivative

Q: Evaluate SSS 5el=²+g²+z?)*² dV over B where B = {(r, Y, z) : z² + y² + z² < 1}. Take 7 = 3. %3D

A: A triple integral involves the integral with respect to the product of the variables x,y, and z. In…

Q: e) Use (; a²p Find the value of Vm at which both of these deriva- T to find aVm tives are zero.

A: I will present e bit for u in the last step....inorder to show u the steps clearly of e bit , I have…

Q: ind a,b and c so that the quadrature formula has the highest degre | f(x)dx % af(-2) + bf(0) + a=1/6…

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Q: Evaluate (xy + yz + xz)dV B = {(x, y, 2) | 0 < ¤ S 7,0 Sys 9,0 < < 9} . Check Answer

A:

Q: Q/ Let X be the r.v such that E (X) = 2 , E(X²) = 2a , E((2+ aX)²) = 2a³ %3D %3D Find the value of a…

A: It is given that, E(X) = 2, E(X2) =2a, E((2+aX)2) =2a3

Q: B (2x + 3y² +42³) dV, where B = {(x, y, z)|0 ≤ x ≤ 1,0 ≤ y ≤ 2,0 ≤ #≤ 3} 08 192 170

A: dv = dxdydz And put the limit of integration.

Q: Q1. If w = f(u, v), u = cosx and v = sinx, show that: d?w v2 fuu + u² fov – 2uv fuv - ufu - vf dx2

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Q: x² Vx + 1 dx (Let u = x + 1, then write x² in terms of u in order for the substitution to work.)

A:

Q: Exercise 3. sin(3z) Let f(z) = and C: |z – n| = 1. Then ſ. f(z)dz = z2(z-n) а. 0 b. 2ni с. — 2пі d.…

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Q: Q3. If w = f(u, v) , u = cosx and v = sinx, show that: d?w v² funu + u? fov – 2uvfuv – ufu – vfp %3D…

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Q: Evaluate II, (z*y +) dz dz dy, where D = [0, 1] × [0, 1] × [1, 2]. %3D

A: Here we have to find the integration if triple integrate: ∭x2y+1zdzdxdywhere D=0,1×0,1×1,2Thus it…

Q: f(t) = t, 0 st < 1 1, t2 1

A: Given function is f(t) = t,0≤t&lt;11,t≥1

Q: i)S V+ 3. + e dy

A: We have to find the integral of given function .   Here student asked only one question so that i am…

Q: X Assume that w =f(s +t) and f'(x) = e dw and ds Find dw ds

A: Use the chain rule of derivative and when differentiating with respect to one variable consider…

Q: a) f(x,y) = xcos(V) + ye*

A: We apply first and second derivative over function

Q: ôw ôw + = 0 for w = Ax, y), x = u – v, and y = v – u and demonstrate the ди ду 6. Show that result…

A:

Q: は F-R m Show that u is 3. sauomphic to F

A: V is isomorphic to F3 means  There is a bijection map between V to F3 such that that bijection is…

Q: 1 Vf(x,y)

A: Given f(x,y)=ln yWe know that ddx(ln x)=1x

Q: Hw I show that' O div (fog) =Pa'g + oP.ug e cur (f) = 0 where

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Q: Q2: dy du (A) Show that if y=csc(u), then -csc(u) cot(u) dx dx

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Q: Q/ Let X be the r.v such that E(X) = 2, E(X²)= 2a , E((2+aX)²) = 2a3 Find the value of a. %3D %3D

A: Let X be the random variable such that, E(X)=2, E(X2)=2a, E((2+aX)2)=2a3

Q: Find r(t) if r'(t) = ti+ e'j+ 3te3t k and r(0) = i +j+ k. r(t) = Need Help? Read It

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Q: dz where a inside r= C z-a 2ni

A: We have to find integration of given function Using Cauchy's Integral Formula.

Q: exy w = f(x,y) = ² sing Rind all P.D.

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Q: Jx (x) = P(1- P) X=1,2,3,.... F, (y,) = ? Fy, (y,) = ? P(Y, <1)=? а. b. С.

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Q: "ind where f(x, y, z) = e²´y and x = Vuv, y = ; %3D dv

A: To find the partial derivative using chain rule

Q: ind V × (V x F) if F(x, y, z) = 9xyj+ 6xyz k. V x (V × F) = ||

A: Topic:- application of derivatives

Q: If Sif(x)dx = 3, then ſ, f(3t + 1)dt %3D Select one: а. 1 ОБ. 2 О с. 3 d. 4 e. none

A: To find the value of the given definite integral.

Q: dy a. Find of the following. dx 1. у%3D 4u? + би — 2 and u — 4x? + 8х + 1 - 2. у%3D uVu +1 and u %3D…

A: Here we have to find dy/dx.     Note : As per our company guidelines we are supposed to answer only…

Q: Find . for (x,y) = x² + y² af af ду' дх Find ду' дх Je Je for f(x,y) : sin xy? x2+1

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Q: f f Find Af = where f(r, y) = In (9r2 + 5y2 – 3r). %3D

A: Here f is two variable function .To find ∆f , first calculate fxx and fyy then add them.To find fxx…

Q: Evaluate p a?y°dx + x°ydy 2,2 3 counterclockwise around the square with vertices (0, 0), (1,0), (1,…

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