using beta function integration Show that: 1 dx = bu xu-1 В (и, т — и + 1) (1 + bx)m+1 By making the following transformation: bx y = 1 + bx

Q: Q2) a) Find Maclaurin expression of f (x) = Cosh (x) b)Find the gradient of the function f(x, y, z)…

A: Part (a) General form of function fx is Maclaurin series is…

Q: If Z1 =1- j3, Z2=-2+ j5 andZ3 =-3- j4, determine in a + jb form: Z1Z2Z3 О а. -5- ј85 О Б. 5+]85 О…

A: We have to multiply the given three complex numbers.

Q: nd the transformation on R' (R3) that reflects at xy-plane, then rota round the z-axis by 90 degrees…

A: Follow the steps below.

Q: Find div F and curl F if F(x, y, z) = x³i - 10j+yzk. div F= curl F=

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Q: дz az Use the chain rule to find and Əs Ət əz Əs əz at = = ¹(=), z = tan u = 3s + 5t, v = 5s - 3t

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Q: 4 2 IF Ø = 2x2² - xy₁ FIND 01111 AT THE POINT (2-2,1)

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Q: Integration of( 3x2-3yz+2xz)dx + (3y2-3xz+z2)dy + (3z2-3xy+x2+2xz)dz along straight line joining…

A: Given: ∫-13∫22∫31(( 3x2-3yz+2xz)dx + (3y2-3xz+z2)dy + (3z2-3xy+x2+2xz)dz )

Q: Determine the function y = eax + b that best fit the data x =(3, 2, 1, 0)T ,y =(µ, 1, e,1/e)T

A: Consider the given information. y=eax+b And, x,y =(3, 2, 1, 0)T ,(µ, 1, e,1e)T=3210,µ1e1e

Q: An analytic function of a complex variable z = x + iy is expressed as f(z) = u(x, y) + iv(x, y).…

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Q: ) Using a drawing technique and a calculus method calculate the gradient when x=3 deitax 6 -10 311…

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Q: True or fulse

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Q: Find Fourier transform for f(t)=t^3-2t

A: Given function f(t)=t3-2t. To find Fourier transform of f(t). By property of Fourier transform,…

Q: For x = x(y + 3), y = y(x - 1), find the trace of the Jacobian at the fixed point x = 0, y* = 0.

A: Given system is x˙ =xy+3y˙ =yx-1 Fixed point :  x* =0, y*=0   Take   x˙ =fx, y,    y˙ =gx, y   then…

Q: Find div F and curl F if F(x, y, z)=xi - 10j+yzk. div F= curl F=

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Q: дz State the multi-variable chain rule for du z=z(t, s), t=t(u, v, w), s=s(u, v, w) if

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Q: Determine whether the following are linear transformations or not. Justify. (1) L(x) = x + 2 where L…

A: The given maps are,(1)  where (2) where The objective is to determine whether the map is a linear…

Q: 2.) у" - Зу' — 2у %3D0 У (0) %3D0, у'(0) %3D 9 ,у" %3D0

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Q: dy/ dx-y/x= -y ^2 /x Is it linear ? does lt become linear with a substitution v = y^ 2? does lt…

A: given equation is  dydx-yx=-y2x

Q: ·볼+1 2x - y dx dy, Use the transformation to evaluate 2x-y where u = v = % and integrating over an…

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Q: -1 A = 0 2) 0. x)T. F(e,) = ( 2

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Q: Laplace Transformation f(t) = t^3 sint f(t) = ( 1 + cosht) ^ 2 f(t) = sin ^ 2 ( t + π ) f(t) =…

A: Ans:Givenf(t)=t3sintThenLf(t)=?we  know  that Ltng(t)=(-1)ndndSnG(S),where G(S)=Lg(t)----(1)Here…

Q: Let z be a differentiable function of z and y related by the following equation: 1+1=(√y+cosh(z)) ².…

A: Given: The equaiton is x+zx-z=y+coshz32. To find: The value of ∂z∂y at the point 3,0,0.

Q: 47. Show that y = x³ + 3x + 1 satisfies y"" + xy" - 2y = 0.

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Q: In integrating the function f(3x + 5)(cos) dv using integration by parts, what would you choose for…

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Q: du/dv = (3u-v)/(u+v) partial

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Q: For the generating function A(z)=- find the corresponding r≥ 0. 1-9z

A: Given: The function generating function is Az=21-9z2. To find: The numeric function corresponds to…

Q: - 4( Let u(t) = 8t i+ (-9)j-8k and v(t)= e'i+9 ej- e "k. Compute the derivative of the following…

A: topic - dot product and derivative of a function

Q: x = s·t u = x² + y³ +z*, {y = s² +² z = s- t

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Q: chain rule to differentiate the following 1 y = sec 4 sec* (√x + 3)

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Q: Find the gradient of the function whose center is at the origin and radius of 7units…

A: We have to find gradient of the function whose center is at origin and radius of 7 units. We know…