6x 1 = (2)ų pue 3 – x = (2)6 hq pelves as a co to on to a los e os (26) = projy (f) Use the inner product =

Q: Let  f(x, y) = sin(15x2 + 3y2) Calculate the quadratic approximation of f at the point (0,0)

A: Given that,  fx, y=sin15x2+3y2 The quadratic approximation of the function fx, y at the point x0, y0…

Q: Get z = f (x,y), x= e° cos t, y = es sin t Show that it's + ) - 2 2 =e 2s + əx. əs

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Q: F(x, y, z) = yzeX²i + e×zj + xyexZk, C: r(t) = (t2 + 1)i + (t² – 1)j + (t² – 4t)k, %3D 0 <t< 4 (a)…

A: Given,

Q: Find the directional derivative of Du" f (2,1) in the direction of: a = 3i + 4j To f(x, y) = InGes…

A: Gradient of a function :  Let f be a differentiable function at  x , y  and let f x , y  have…

Q: - Find div F and curl F if F(x, y, z) = 10y¹z7i – 17xªzºj – 3xyễk. div F= curl F=

A: The general form of a vector-valued function in three dimensions is given by F=F1i+F2j+F3k, where…

Q: Show that ƒ(z) = 3x² + 2x − 3y² − 1 +i (6xy + 2y) is differentiable at every point in the plan -

A: The given function is f(z)=3x2+2x-3y2-1+i(6xy+2y)...(i).

Q: Let 7(t) = (– 5t4 – 4, – 2e“, 2 sin(3t)) Find the unit tangent vector T (t) at the point t = 0 T (0)…

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Q: Find the work done when a particle moves along the x-axis from x= 1 to x= 3 under the action of a…

A:

Q: Q2// B :- If u+v3e"cos y and u- v=e' sin y find the Jacobain of the function alu,v at dx.yl (x.y)…

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Q: 13 Find the linearizatian z=L(x.y) f the function 2=f(x.y) =4x²-y²42y at the point (x.y) = (3,2).…

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Q: If A = yz(^2) i - 3xz(^2) j + 2xyz k , B = 3x i + 4z j - xy k and ∅= xyz , find (a) Ax (∇∅), (b)…

A: Since you posted a question with multiple sub-parts, we will solve first three sub-parts for you. To…

Q: Integrate the function f(r,y, z) = Over the entire 3D coordinate system, i.e., all of R'.

A: We have to integrate the function fx, y, z=1x2+y2+z21+x2+y2+z2 over the entire 3D coordinate system,…

Q: L(x) = b) Use the linearization to approximate 125.1 ~

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Q: alu,v at dx,yl Q2// B :- If u+v=e"cos y and u- v=e" sin y find the Jacobain of the function (х,у)…

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Q: - 4( Let u(t) = 8t i+ (-9)j-8k and v(t)= e'i+9 ej- e "k. Compute the derivative of the following…

A: topic - dot product and derivative of a function

Q: f(x, y) = xsin²y + y² cosx, Find fxy a. sin² y - y² cosx b. 2xsinycosy-2ysinxcosy c. 2sinycosy -…

A: We need to find fxy.

Q: The direchional derivative of the salan funchion at (l,-1,0) in the direction (i-j+2k) is xy- z- xyz…

A: Given that  Let f(x,y,z)=x^2y-y^2z-xyz To find the directional derivative at point

Q: Prove that the directional derivative of f(x, y) = y + 2xy³+x²y2 at point (0, 1) in the direction…

A: The gradient is just the vector of partial derivatives. The partial derivatives of f at the point…