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: Let D, be the linear transformation from C'[a, b] into C[a, b). Find the preimage of the function.…

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Q: kh= •a+h [ath 2xƒ(1) √ √ 1 + (ƒ' (1))² dt 2лf(t).

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Q: Use the intermediate Value Theorem to show that between x = 0 and x = 1, the function f(x) = 3 sinh…

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Q: Find f. f"'(t)  = t   - √t

A: To find f"(t) we integrate f"'(t)

Q: Find the tangent line approximation for V5 + x near a 4.

A: Find your answer below

Q: Draw a direction field (slope field) of y' = x. Use all 25 grid intersections. 2 1 2 X

A: Note: Slope fields allow us to analyze differential equations graphically. When an explicit solution…

Q: 3.1 (x+1) (x'+5x+2) ふeren ta ee

A: Topic = Derivative As per guidelines , At a time only one question can be answered.

Q: 4. Integrate the function f(z) = z² + 2z from z = -i to z = 1 in two ways, once along a straight…

A: The objective is to integrate the function fz=z¯2+2z from z=-i to z=1 in two ways, Once along the…

Q: Plot the slope field of y=x+y using slopes m = -3, -2,-1,0, 1, 2. Sketch integral curves for…

A: First we plot the slope field and then plot the curve .

Q: Evaluate: ²₁¹ (x² - y²) ²1 x+y du du dt

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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: ZWVX TUY, UV XY, and ZVXW ZTYU. Complete the proof that ATUY AWVX. Y. Statement Reason ZWVX E LTUY…

A: Given,

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

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Q: Given the preconditions for x and y as |x – y| ≤ 200, |2x + y - 150| ≤ 250, show the post-conditions…

A: Given that, z=3x2+y2+3xy-7x-8y+10 Subject to  x-y≤200 2x+y-150≤250

Q: Suppose the velocity of a ninja is given by v = ft, 3t², sin(π) at time t. If the position of the…

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Q: Evaluate This Integral if curve C consists of curve C₁ which is a parabola y=x² from point (0,0) to…

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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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Q: Use the Cauchy-Riemann equation to determine if the function f(2) = x³ – i(2 – y)³ is analytic or…

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Q: Use Linear Approximation to estimate the change, Az, in z = 8x2 + y? as (x, y) changes from (2, 3)…

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Q: Calculate Vf when f 3x 2- y z' + 4x'y + 2x - 3y - 5 at the point (1, 1, 0).

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Q: Determine the NATURAL cubic spline S(x) that interpolates the data f(1) = 1, ƒ(2) = 1, and f(3) = 0.

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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.