ind the linear approximation of the function at the given point. x_ v) = -4 sinx+ 7 cos y at (0, 7 L(x, y) = -4x+ 7y + 7 L(x, y) = -4x - 7y + 7 n L(x, v) = 4x+ 7y +

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A:

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A: Given : F(x, y, z)=(x²  + 3y ,  y² -4z ,  sin(x )cos(y) - z2 )  Now we find div F = ?

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A:

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A: Differentiate both sides with respect to t.

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A: For the solution of the problem follow the next step.

Q: 4. Let f(x, y) = 2TY x = In 2 g and y = In s. . a. Find the equation of the tangent plane to f(x, y)…

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Q: What is the maximum value of f(t) = sin t + cos t in the interval 0<t< =?

A: Given; f(t) = Sin t + Cos t.

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A: Use formula of  linear approximation

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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

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A: Topic- Application of derivatives

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Q: Use a local linear approximation of the function f(x) = VI cos[(V2x)T] approximate v3.98…

A:

Q: 4. If f is a differentiable function of a and y with w f(x, y), x =r cos 0 and y = r sin 0, %3D show…

A: To verify the given relations between partial derivatives.

Q: Using an appropriate linearization, the local linear approximation of f(x)%3D+ cos r at is 2.

A: To determine the linear approximation of the function.

Q: Use the Chain Rule to find dz/dt. z = sqrt 3+ x^2+y^2, x= 3 ln t, y= cos t

A: Use chain rule to differentiate z

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

Q: sin(t) et, X2 sin(t)- cos (t) and X3 D sin(t) + cos (t)] 0. Given that X, cos(t) sin(t) + cos (t)|…

A: The problem is wrong, three vectors are not linearly independent.

Q: Use a local linear approximation of the function f(z) = VI cos[(V2r)] at some approximate v3.98…

A: To use local linear approximation of the below function to approximate 3.98cos7.963π. fx=xcos2x3π

Q: F(t, x, y, 2) = [0, cos(t), sin(t)] x 7, 0<t<

A: Solution

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

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Q: The linearization of ex at x = 0 Derive the linear approximation ex = 1 + x at x = 0.

A: Given, ex ,x=0 We know that, The formula for the linearization is, Lx=fa+x-af'a

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A: Given: dx/dt - 2y = -sin(t), dy/dt + 2x = 5cos(t)

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Q: 2. Let L:= D2 - x-D+4x2. Verify that Ly 0 where y(x) = sin(x). %3D %3D %3D

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Q: Evaluate the line integral F. dr where F = (3 sin x, 3 cos y, 10xz) and C is the path given by r(t)…

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

A: using CR equation we get....

Q: Find fa, fy, and fz. f (x, y, z) = z In(xʻy° cos(52)) 4,3 COS x*Y fn = fy = fz =

A: Please refer the attached image for complete solution.

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Q: Show that F = (2x - 3)i - z j + (cos z)k is not conservative.

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Q: The functions cos r and cos- are linearly dependent (0, ) on

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Q: is function oF x $ y xz + y In x = ze-sin (xy) D. Ausumo that z Find zx iF

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Q: Use the Chain Rule to find dz/dt.z = sqt(8+x^2+y^2,    x = 4 ln t,    y = cos t dz/dt=

A: Please refer to the image below

Q: Using an appropriate linearization, the local linear approximation of is f(x) = T+ cos r at 2.

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A: We have to find out

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A: Answer is given below

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Q: 2. Integrate: a) Sx cos(x²) dx g) [3 cos(2nx) dx b) S tan³ x sec²x dx h) Se2% sin(e²*) dx c) S cot x…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: If f(x, y) the total differential of f at (0, ) i 16e Cos x + 7 cot y, then the total differential…

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