Integrate f(r, y, z) = for 0

Q: Use Green's Thoerem to evaluate F dr. where F(r, y) = (-3Vx² + 2, 7 tan '(x)) and C is the triangle…

A: We have to evaluate by Green's theorem.

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(r,t) = cos(3r) exp(4t) %3D fi(x,t)+ frz(x,t) = f(r,t) %3D

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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 the directions in which the function f(x,y) = x²y + e* sin(y) Increase and decrease most…

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Q: B) r(t) = (4 cos t, 4 sin t, 16)

A: We consider x=rcos(theta) and  y=rsin(theta)  Therefore r^2=x^2+y^2

Q: Sketch the curve r(t)=f°i+tj and indicate the orientation. Find r'(t) and sketch r(1) & r°(1).

A: First we will plot the given parameters.

Q: Find f. f "(t) = 2et + 5 sin t, f(0) = 0, f(x) = 0 f(t) =

A: We can solve the given problem using the concept of application of integral.

Q: (Calculus) The tangent vector to (x(t), y(t)) is (x'(t), y'(t)). The tangent vector's length ||(x',…

A: Given that the tangent vector to and is the speed of the point along the curve at time t .Here also…

Q: Find f. f(t) =|| f"(t) - 3et+ 5 sin t, f(0) = 0, f(T) = 0

A: To find f.f''t=3et+5 sin t, f0=0, fπ=0

Q: The temperature on a cubic box [0, 4] × [0, 4] × [0, 4] (measured in meters) can be described by the…

A: Function, Tx, y, z=x2y+y2z

Q: L (sin? t) What is f (t), f' (t) and f (0) ? O b) O a) f (t) = sin t, f' (t) = 2 cost, f (0) = 0 f…

A: We will find out the required solution.

Q: r(t) = (4+t)i+(9+ln(cos t))k, -pi/2 < t < pi/2 Find principal unit  normal vector N for the curve…

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Q: Find f. f"(t) = 5et + 4 sin t, f(0) = 0, f(1T) = 0 f(t)

A: topic- differential equation

Q: Encuentre TLt), NCt) B (t) de cLE) = ( cost , sent, t)

A: We will use the respective definitions.

Q: f(x, y) =- sin xcos y, then

A: The given function is: f(x,y)=-sin xcos y To find ∂2f∂x2. Here, note that y is constant w.r.t. x.

Q: The maximum directional derivative of f (x, y, z) = x² sin(zy) – yx + 10 | at (-1, 2, 0) is

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Q: Find the maximum rate of change of f(p, q, r) = arctan(pqr) at the point (2, 6, 2).

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Q: 5 Let f(x) = - 5x° /¤ +

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