Show that the following line integral is path independent and evaluate its value. Show the details of your work: r(3,5) cosh 3 (10xdx+6ydy) (0,0) BIEE / 2 Paragraph 00

Q: ds if s = Find dt 7t + 3 ds dt II

A: We have given;

Q: x2-3x+1 i) S xln²xdx and ii) S7 dx. (x+2)(x2+1)

A: Given: ∫x ln2 (x) dxFormula: (ln (x))'=1x∫ x dx=x22+C

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Q: dP dt т 1- kP 1- M

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Q: Use the linear approximation to approximate (123)/3.

A: Let's find.

Q: The function z is defined by z(x, y) = x y-3 y Find A z and dz when x= 3, y= 5, Ax = - 0.04 and A y…

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Q: 2 - ) at x = 4 1+ x)

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Q: Find the Atend and matnix gF

A: Given a T be a linear transformation and Tx,y=x+y,y−x We have to find the standard matrix of T Let…

Q: Show that (0, 1) ~ R.

A: We need to show that the open interval (0, 1) and R( the set of real numbers) are equivalents. The…

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Q: Show that the function u(x,t) = t/2e-*/4 (t > 0) satisfies u, = uxx.

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Q: Find the function r that satifies the following condition. r'(t)=(3t2,4t3,2t); r(1)=(-2,-5,-9)…

A: Given,          r't= 3t2 , 4t3 , 2t  , r1=-2,-5,-9

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: 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: f lx.y) = x³ - byt +ll Investigate the local + 3xy" - 6x² extremum paints ofthe function determine…

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Q: Plz asap handwritten solution acceptable Will definitely upvote

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Q: if r'y-- 2y + 1.

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Q: Find the domain of Hi function fr w =J 2x+3 -1

A: It is given that the function fx=2x+3-1. Find the domain of the function. It known that the root of…

Q: Use the method of Characteristic to solve U t tuux = 2t, u(x, 0) = 3x.

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Q: 4 + cos t -dt 1 – sin t

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Q: Determine the vesulting equaton Determine the vesulting equaton after using the suitable…

A: We have to find

Q: PLS HELP ASAP ON ALL

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.