What does parseval's identity imply about relationship between the dot products x · y and [x]ẞ· [y]ẞ?

Q: Use Green's Theorem to find f. [(2x – y+ 4) dx + (5y+ 3x – 6) dy] around a triangle in the xy plane…

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Q: The curl of- yi+z+xR"

A: In this question, we find the curl of the vector function by using the determinant method.

Q: Find div F and curl F if F(x,y, z) = xzºi+ 5y°x²j+ 5z?yk.

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Q: Is the function eiz² holomorphic in C? Explain why. What are the Cauchy-Riemann equations for eiz?

A: Given function : f(z) = ei z2

Q: Find the slope of the tangent in the positive x-direction to the surface z = 3x - 6xy at the point…

A: We have to find the partial derivative with respect to x

Q: what is the area of the rotational surface formed by rotating the part of the function y= x^3/3…

A: We apply the above formula to solve this

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: Z=x+y+ cos(x+y)

A: Given,        z=x+y+cos(x+y)

Q: Find the surface area of the surface when f(x)=x3 on [0,2].  Is rotated about the y-axis and about…

A: Use surface area formula

Q: (a) S,(Iz – il2 – z) dz along the semicircle y = 1+ et“, 0 < t < n; -

A: ∫γz-i2-zdz=∫0π1+eit-i2-1-eitieitdt=∫0π1+cost2+sint-12-1-eitieitdt=∫0π1+cos2t+2cost+sin2t+1-2sint-1-e…

Q: Use polar coordinates to set up and evaluate the double integral f(x-

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Q: Use Green's Theorem to calculate line integral o sin(x²) dx + (3x – y) dy where C is a right…

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Q: Find the surface area for the object obtained by rotating y=7x+2 about the x-axis over the interval…

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Q: over the open surface S given by the upper part (only) of the intersection of ti of the function z =…

A: Introduction: Stokes Theorem (also known as Generalized Stokes Theorem) is a statement about the…

Q: Find an antideriuative Flx) of the functian f(x) = 8 sinx such that FlO)=D1 %3D 13 + COSX

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Q: Find div F and curl F if F(x, y, z) = 13y'z4i – 16x4z10j – 3xy'k. - - div F= curl F=

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Q: 6. Let f(x,y) = sin(x + y) + arcsin (xy) a. Find the linearization L(x,y) at the point (0, ")

A: We have to find linearization of given function f(x,y): Concept: The linearization of a function…

Q: What is the ALGEBRAIC RULE for a REFLECTION over the x-axis? (х, у) —

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Q: Write an equation in general form of the tangent plane to the surface x^2+siny + z^3 = −4 at the…

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Q: 1) Find the area of the surface generated by rotating the function y=x^3 about the x-axis over 0≤x≤3…

A: As this is a multiple question according to the Bartleby Answering rule, only first question and its…

Q: An integral expression for the area of the surface generated by rotating the curve X =Vy , 1sys8…

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Q: za z = e

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Q: Verify Green's Theorem in the plane for F = -3y³i+ (3x3 + cos y)ĵ where C is the circle x² + y² =…

A: In this we have to verify green theorem.

Q: find the centroid of the thin plate bounded by thegraphs of the given functions. Use Equations (6)…

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Q: Integrate f(x, y) = (x + y + 1)- 2 over the triangle with vertices (0, 0), (4 , 0), and (0, 8).

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Find the guneral antiderivative of the funchion. (check your answar answer by differentiation.) 14)…

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Q: Use the canonical Euler equations to find the extremals of the functional SV + ya Vi+ ya dx,

A: Consider the equation

Q: calculate div(F) and curl(F). F = (xy, yz, y² – x³)

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Q: (a) If f(x,y) = e" siny – e sinx then verify that fæy = fyx. %3D -

A: Given that  f(x,y)=e^xsiny-e^ysinx To verify the fxy=fyx

Q: Double integrate under z=xy, above the triangle with vertices (0,1),(0,4),(1,1).

A: We have to find the volume by double integration

Q: (b) Use Leibniz's product rule to derive the quotient rule y du- v dy d YY

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Q: Find the approximate roots of y = r - a +x – 3 between r = 2 and z = 2.5 by using either the…

A: Bisection method: Let f(x)=0 be equation, to find the roots of equation in interval a,b. Let us…

Q: Locate the centroid of the shaded area shown. y%3D 4 3 -3 -4T-

A: The centroid represents the centre point of the curve . For example if we have a point in…

Q: Compute , F · dS for F = (sin(y), sin(z), yz), S being the rectangle 0 < y < 3,0<z< 6 in the…

A: Given :- ∬S F. dS for F = (sin y , sin z , yz) S being the rectangle 0≤y≤3 , 0≤z≤6 in the yz- plane…

Q: Use Green's Theorem to evaluate 5x*dx +xydy where C is the triangle with vertices (0,0), (1,0),…

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Q: find div and curl F F(x,y,z)= 7y3z2i- 8x2z5j-3xy4k F(x,y,z) = exyi-cosy j +sin2 z k

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Q: Express x = In(3t), y = 5 – t in the form y = f(x) by eliminating the parameter. %3D y =

A: Given that x=ln(3t) and y= 5-t we need to write y=f(x) by eliminating the parameter  Now , x= ln(3t)…

Q: 13. Verify if div(curl F) = 0 for F = (x - y) i+ (x + y)j+ zk. %3D

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Q: 1+iz if w= Find the image |z|<1 1-iz

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Q: Find the image of y = 1 under f(z) =1/z %3D %3D

A: Image of y=1 under f(z)=1/z

Q: a Use parseval's identity to prove that dt TC (a² + )(b + ?) 2ab (a + b)

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Q: How are dot products useful?

A: Two vectors can be multiplied using the dot product. The dot product is written using a central dot.…

Q: The imaginary part of z=x+iy is x

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Q: the surface area of a .17 rotating the curve y = x power 3 around the x - axis between the points…

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Q: find the centroid of the thin plate bounded by thegraphs of the given functions. Use Equations (6)…

A: First, we need to find a mass of the plate.

Q: An open rectangle box with volume 2m2 has a square base .express the surface s of the box as a…

A: Please find hand written solution.

Q: 3. f(t) = 3sin2t

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Q: Find div F and curl F if F(x, y, z) = 16y°z³i – 9x°z°j – 7xy'k. - - div F= curl F=

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Q: An integral expression for the area of the surface generated by rotating the curve X =Vy, 1sys8…

A: According to our policy we are allowed to answer only one question at a time. Kindly repost other…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.