Find V²f by the formula V²ƒ =div(grad f) given f(x,y, z) = e³wyz grad f = [| V²f =

Q: given f (z) = 32² – 6z + j3, what is the value of u(3, 2)

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Q: Suppose that f(r, y) = 3x y + 8a? + 4y? then find the discriminant of f.

A: f(x,y) = 3x²y² + 8x² + 4y² So, fx = 6xy² + 16x  &, fy = 6x²y + 8y  &, fxx = 6y² + 16 &,…

Q: Find ∇2f, given that f(x, y, z) = 1 / (x2 + y2 + z2)1/2.

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Q: Q2/ A/ Find the and ar * iff (x.y) = x - xy, x=r² +s and y =r-s as

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Q: Find the values of the constants a, b, c so that F = (axy + bz*)i+ (3x² – cz)j + (3xz? – y)k Is…

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Q: Hawis Find d Vand V2if vI+2V2=31-k and 3V-V2 si+j+k

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Q: given f (z) = 3z? – 6z + j3, what is the value of v(2,1)

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Q: d²y y = f(x) and x = e', prove that = xf'(x) +x²f"(x). %3D %3D dx2

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Q: For the function f(x,y,z) = In (5x + 4y + 9z), find f,, fy, and f,.

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Q: 03. Find se and *. If f(x,y) = 2e* + Iny² ,and x = 2t + r2, y = ; %3D at r+1

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Q: For the function f(x,y,z) = In (5x + 7y + 1Oz), find f,, f, and f,.

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Q: What is the domain of r(t) = e'i + j+ (t + 1)~³k?

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Q: Ifx' +y +z -2aņz =1, then show that V1-x dy 1- y V1-:

A: We have to use the given condition x2+y2+z2-2xyz=1 to find this.

Q: TF x and y are orthon ormal rectors then Pind Value of Ilx+y12 - ||x-Y2

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Q: Given the multiple variable function f(x, y, z)= Ax*e» - Bz cosx*y°)+Cx*y*z?, where the coefficients…

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Q: d²y Given that x3 + y³ = 2, prove that 4х %3D dx2 y5

A: Given problem:-

Q: For the function f(x,y,z) = In (6x + 7y + 4z), find fx, fy, and f,.

A: Given: f(x,y,z)=ln(6x+7y+4z)To find the fx, fy, and fzddx (ln x)=1x

Q: f. . Prove false by creating a counterexample: 9(AUB) C P(A) U P(B)

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Q: Prove that : V.(V×A)=0

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Q: Given f(x, y, z) = V 4a? + 2y? + z², find fz(x, y, z) = fy(x, y, z) = f:(x, y, z) = |

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Q: f) Given w=(x+y)/(z-3y) , Find dw

A: Total derivative

Q: d²y Given that x +y³ = 2, prove that dx2 4.

A: Given: x3+y3=2   As we know that; The Power rule: ddxxn=nxn-1 The Quotient rule: fg'=f'·g-g'·fg2

Q: What does dr stand for in terms of r(t)?

A: Given: What does dr stand for in terms of r(t)?

Q: Find the absolute maxima and minim uל םיל É(x v) = x2 • 1x + y²+ 20y +7 on the rect

A: To find the absolute maxima and minima of the function on the given function.

Q: Q3. Find af and at se If f (x, y) = 2e* + Iny2 ,and x = 2t + r2, y = ar r+1

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Q: d²y Given that x3 + y³ = 2, prove that 4x dx² y5

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Q: f[x'+zy2,y²2x2], then prove that [y?-zx] (a?-yz] dy [z-xy] du -o. If

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Q: The x, y, zER, subject to the condition yz + zr + xy = 12. Then greatest value of rvzis (a) 6 (b) 8…

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Q: ||| V3(x² + y²)dV, where V is bounded by y = 2x² + 2z² and y = 8.

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Q: Prove that r(v) : dx, v> 0.

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Q: Find V · (V × F), if F(x, y, z) = 6e²*i+ 5xe"j – 2ev³k. %3D -

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Q: Find and given f(x, y) = y" In(x²) + - Va 8y

A: Given: Function in x, y is given.          fx,y=y7lnx2+9y3-x47 Objective is to find,…

Q: Q3) for f(v) = sec2 (3v-1) and g(v) = tan2(3v- 1) show that %3D S(v) = g'(v).

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Q: Let f(x, y) = x² + xy + y² where x = 3(t + s) and y = e2st, find . as

A: we have given f(x, y) where x and y are function of s and t.  We have to find the partial derivative…

Q: Find the linear approximation of y = V1+ x at x = 0 and use it to approximate V1.05 7.

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Q: x² + 5x ,14.f(c) = = 14 f(x) on interval %3D %3D x - 1

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Q: Q3: Find the value of n which F(x, y, z) = (x +y +z*)" to satisfy fxx +fyy+ fz= 0. 1

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Q: Find the minimum and maximum values of f(x,v) = x2 - 3y + y³, x² +4y? < 36

A: Given,         f(x,y)=x2-3y+y3  and   x2+4y2≤36.

Q: Let y = f(x1, x2, w), where x1 = 2w2 and x2 = w+1. Find dy/dw.

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Q: f(x, -0.0494 -0.3662 etter estimates by using Ar = 0.01 and Ay = 0.01. %3D 0.0516

A: Here we have to use difference quotients with ∆x=0.1 and ∆y=0.1 to estimate the fx(1,3) and fy(1,3)…

Q: af when s = 1,t = 1 for f (x, y) = x³ – 3xy - 6x + 6y ,x = 2t + s, y = 2s – t. a) Find as

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Q: 2R then the constants R TCX If f(x) Rsin .2 S,f' and f(x)dx and S are respectively.

A: Introduction :Here we have asked to find the value of R and S

Q: Find V · (V × F), if F(x, y, z) = e2²i+ 7xe'j – 2e²k. - V·(V × F) =

A: Solved below

Q: Consider the finction f(x, y) = 6y² + 4x² – 12xy – 4y. Then:

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Q: Find the largest domain (in R²) for the function 1+ Vx + Vy x² + y? f(x, y) =

A: The domain are those values of x,y; such that f(x,y) is well defined. Well defined means that the…

Q: Let f(x, y, z) = 3x?y+ yz3, where x = 3 – t2, y = 2t + t3, and z = V1+ 3t. Calculate when t = 1.

A: NOTE: Refresh your page if you can't see any equations. . here we have . the given function is…

Q: Q2: Given y = f (u) and u g(x), find dy/dx: y = 2u3, и %3D 8х — 1

A: Differentiate

Q: Q2: y" + ay' + by f(t) Find a,b and f(t) so that Ypı = et +t? – 1, Yp2 = e2t + t2 – 1

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