Q: Please
A: Please refer to the image below
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A: Explanation of the answer is as follows
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A: We will solve the definite integral.
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A: topic- average value of function over interval
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A: The given definite integral, ∫-10x24x3+53dx
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A: Note that, according to Bartleby guidelines, we can answer only the first question in the case of…
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A: In this question , we can set up the integral to find the area of M .
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A: We need to find force and work.
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Q: Sketch the region enclosed by y = e, y = e¹0, and x = 1. Find the area of the region.
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Q: Find the curl of the following vector field: F = (z, 2y, -3x)
A: Follow the procedure given below.
Q: 8. For what value of the constants A and B is the function f continuous on (-∞, ∞)? Ar + B for r 2
A: Please see the the answer below.
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A: I am attaching image so that you understand each and every step.
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Q: Find the general solution. ܕܙܐ
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- What does it mean for the differentiability of a function if the Cauchy-Reimann equations (Ux = Vy and Vx = -Uy) do not hold?let f(x,y,z)=ax3y + by2e1-z+cze1+z be a function . Find a, b, c, so that the maximum value of the directional derivative at the point P0(-1,3,1) in the direction of the line parallel to 0x axis 21.A smooth curve is traced by vector-valued function R(t) with R(1) =<2,-1,1> with derivative R'(1)=<1,-2,-1>.Let g(t) = esin2t. Find (R o g)'(0). hint: (R o g)'(t) = R'(g(t)) g'(t)
- Use Green's Theorem in the form of this equation to prove Green's first identity, where D and C satisfy the hypothesis of Green's Theorem and the appropriate partial derivatives of f and g exist and are continuous. (The quantity ∇g · n = Dng occurs in the line integral. This is the directional derivative in the direction of the normal vector n and is called the normal derivative of g.)can i get help with this line integral vector calculus question4 Find the directional derivative of f (x,y)= 2x^2 y^2 -3xy at the point (1,-1) in thedirectiona. of vector v =<4,3> and toward the origin.
- Suppose that z is an implicit function of x and y in a neighborhood of the point P = (0, −3, 1) of the surface S of equation: exz + yz + 2 = 0 An equation for the tangent line to the surface S at the point P, in the direction of the vector w = (3, −2), corresponds to:Define Wronskian of Linearly Dependent Functions?Use Theorem Directional Derivative to find the directional derivative of the function at P in the direction of v f(x, y) = x2y, P(−5, 5), v = 3i − 4j