The absolute value of the integral 5z3 + 3z2 -dz, z2 – 4 over the circle |z – 1.5| = 1 in complex plane, is (up to two decimal places).

Q: Evaluate the volume between the surface z = 3 + 2x + xy, and the rectangle in the xy plane given by…

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Q: Let Z₁, Z2, Z3 be three complex numbers and a, b, c be real numbers not all zero, such that a + b +…

A: Given Data :   Z1 , Z2 , Z3  are complex numbers a, b, c be real numbers not all zero a+b+c=0 az₁ +…

Q: Plot the graphs of f(x) = x^2 and y(x) = √(4-x^2), where x [-2; 2]. Calculate analytically the…

A: The objective of the question is to plot the graphs of the functions f(x) = x^2 and y(x) =…

Q: What is y(x) (i.e., y as a function of x) given that dy dx where you are given the boundary…

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Q: Consider the line element of the sphere of radius a: ds2 = a2(dθ2 + sin2 θ dØ2 ). The only…

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Q: What is the equation of the sphere with center (1, –2, 5) and radius 9 ? O (x+1)² + (y – 2)² +…

A: Radius of sphere is 9  and equation of the sphere can be calculated as,

Q: Evaluate the following integral: Answer: Check [ ∞ x³8(x + - 2)dx =

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Q: A triangle in the xy plane is defined with = (0,0), (0, 2) and corners at (x,y) (4, 2). We want to…

A: The triangle has corners at (x,y)=(0,0), (0,2) and (4,2). We have a function f(x,y) which we need to…

Q: Determine the following indefinite integral up to a constant c: ∫(sin(3?+7)+cos(7?+3))?? Select…

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Q: If v= (2+i, 3-2i, 4+i) and w = (−1+i, 1−3i, 3-i), use the standard inner product in C³ to determine,…

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Q: ds²=- Consider the following spacetime: dr² dt2 · + r² (də² + sin² 0 dø²), where > 0 is a constant.…

A: Step 1:Step 2:Step 3:

Q: find the commutator [Lz,cosφ]

A: The commutator of two operators A and B is given by

Q: In this problem you will use the bisection method to compute the eccentric anomaly E in equation (2)…

A: To solve for the eccentric anomaly E using the bisection method, and subsequently compute the x and…

Q: Consider the curve described by the parametric equations x = 3 cos t, y = 2 sin t. Compute the slope…

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Q: Find the distance from the point (-7,2,8) to the yz-plane

A: The objective of the question is to find the distance from a given point to the yz-plane in a…

Q: Use a proof by contradiction to show that for all integers n, n²- 2 is not divisible by 4.

A: Introduction: Suppose the given function n2-2 is divisible by 4 then we can check whether it is…

Q: Find an equation for the plane through the points (-6, 8, –1) and (-1,3,–8) and perpendicular to the…

A: The equation of the perpendicular plane is-4x-3y+8z=0Equation of a plane is given…

Q: (a) For what range of v is the function f(x) = x" in Hilbert space, on the interval (0. 1)? Assume v…

A: (a) The vector space of all square-integrable functions is Hilbert space. The given function is,…

Q: Consider the real part of the spherical harmonic Y1, + 1. At which values of do angular nodes occur?

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Q: Describe all vectors in span{(3,0,2), (-2,0,3)} (so computationally what do the vectors look like?).…

A: Given span: 3,2,0,(-2,0,3)

Q: (b) Write a necessary condition for a transformation (q,p) to (Q,P) to be connonical. Prove that…

A: Here the transformation has to be done from (q,p) to (Q,P); The condition for it to be canonical is,…

Q: The distance from the point (-8,-7,-2) to the yz plane is: ?

A: The objective of the question is to find the distance from a given point to the yz plane in a…