Evaluate the the integral ff, (x²+y+z)dS where S is the portion of the plane z = x + 3 that lies inside the cylinder x² + y² = 1. To 1 decimal places the voll given by (Answer in the form (123456.7))

Q: b) Express the area of the pool, A in terms of I and r. c) Hence, or otherwise show that A = -² +…

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Q: 2.6 Find the area of the parallelogram represented by u = 2i − j + 4k and v = i + 2j − k using the…

A: To find the area of the parallelogram represented by by using the proper method.

Q: z = tan¯1(4 – j7)

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Q: nter the exact answer. Im z? dz

A: Given, the vertices of the triangle are 0, 2, 2i.

Q: dz at the point (3,2, 1), where z is defined implicitly by the equation z +z²x² – y = 8 Calculate dx…

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Q: Sinlxy). lnx dx 19141 to be investipa te the uniform Convergence of ne parametric intepral)

A: Given integral is, ∫01sinxylnxxdx Since, the given integral is improper integral so applying the…

Q: Suppose that a, b € Vand S € V2 are given. By expressing these quantities in a coordinate frame, or…

A: Given: The given identities are a) S(a⊗b)=(Sa)⊗b b) (a⊗b)S=a⊗(STb) c) (a⊗b)T=b⊗a To find out the LHS…

Q: Derive the De Moivre's Theorem with detail Explanation?

A: Statement: For any real number x, we have (cos x + i sin x)n= cos(nx)  i sin(nx) Or, (eiθ)n=eiθn…

Q: Exercise. Find Hhe value of the integral 3. dz Č (z-1)(z+9) taken Counterclockwise arcund the…

A: answer

Q: part öf the cicle42| = 2 in the first quadrant. Find an upper bound for the integral . b) Let C be…

A: Solution-(a) the path of integration has the length L=4π Upper bound M for the function =1z2+1;z=2…

Q: Use De Moivre's Theorem to find the fourth root of Z = 8i(3 + v2).

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Q: 10e? dz by residue theorem, where C'is the contour z| = 2 1:4 + 52ª Evaluate

A: Complex integration

Q: Evaluate xy ds, where C is describe by æ = 4t, y= 3t, 0 <t<1. Enter your answer as a number in…

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Q: x y ● = Find the dot product of 1 18 0 — -2 and y = 1 2 4 ●

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Q: Sketch the following given that Z = x + yi (2-3) (2+3) = 2

A: Given ,                 (z-3)(z+3) = 2   ;    z=x+iy

Q: baphress -4i in esponenial form reio the Qunge OLOC2TI in

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Q: - Find a formula for the function T(x, y, z) of three variables that gives the square of the…

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Q: 2. Which cannot be represented by a scalar? a. speed b. velocity с. area d. mass

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Q: Find y'(0) and y"(0) from the following table ofvalues: X 0 1 2 y 4 8 15 3 4 7 6 5 2

A: From the given table upper digits are values of X and lower digits are values of Y(X).

Q: TEST FOR HOMOGENEITY: 4. e √x x-2xy x - y

A: A function f(x, y) is said to be homogeneous if f(Kx, Ky) = Knf(x, y)  where n is any real number…

Q: 1 in 1in y 1 in 3 in 1 in X

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Q: b) Express the area of the pool, A in terms of I and r.

A: We need to solve the part (b) of the question :

Q: 3 b. (Зетi

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Q: Find the surface area of the part of the plane z = 6 + 7x + 3y that lies above the rectangle [0, 4]…

A: Given equation of plane  z=6+7x+3y defined over D=[0, 4]×[0, 4] Now differentiate partially with…

Q: Use calculus to show that the maximum possible area of a triangle with one vertex at (0, 0) and the…

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Q: Find curlF for F = xyz?i+ x*yz?j+ x*y?zk.

A: Given, F→=xyz2i→+x4yz2j→+x4y2zk→ Used formulas, ∂∂xxn=nxn-1