Consider the diagram and flow-proof below. Given: ZPTS = LPLE AP bisects

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A: Consider the provided question, We need to prove that the rectangle that has maximum area for a…

Q: show Hat the (Rang) ra bounded Linear operater Ti x-oy need not be closed in y. Hint useTe e Yang…

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Q: tlowing is I equivalent 8 So 长-St e "e cost dt?

A: we know that Lft=∫0∞fte-stdt

Q: Evaluate (yzi+yj+zzk) - dA, where S is the boundary of the cube defined by -1<IS2,-1 SUS1, and 0<…

A: We can use gauss divergence theorem to evaluate the surface integral.

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Q: Evaluate SSS e² dV where E is enclosed by the E paraboloid z = 1 + x² + y², the cylinder x² + y² =…

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Q: 4. Give an example and a proof to not increase intrinsic distance.

A: We have given statement that Local isometries can shrink but not increase intrinsic distance. We…

Q: wo straight roads that meet at right angles. 89500 x m² x 0 100 200 300 400 500 600 700 800 900 1000…

A: A table of values of x and y as: x 0 100 200 300 400 500 600 700 800 900 1000 y 125 125 119 113…

Q: h ਹ 2 ((a re) 7

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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: State and prove Green's identity in an enclosed Region Q

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Q: 3. Using a substitution, show that the following shaded areas are equal. You do not need to compute…

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Q: a70 clam cniti nes on fisunif

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Q: Let foo = x-x -1,06 <2 Use the Fixed-Point iteration method to approx imate the roo- of FOu accurate…

A: We have to use fixed point method to solve given equation.

Q: Exercises:

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Q: 4) Let B be a sphere with radius a and center 0 and r be the radial dis- tance. Applying Green's…

A: Consider the provided question, Let B be a sphere with radius a and center 0 and r be the radial…

Q: Let M and m be the maximum and minimum values of Ax, y) = 5x + 4y on the region x +y < 49 . Then…

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Q: Evaluate xz dV, where W is the domain bounded by the elliptic cylinder += 1 and the sphere x² + y² +…

A: The domain W is bounded by:The elliptic cylinder , and the sphere in the first octant.To Evaluate:…

Q: Can there exist a AROS in which the trisectors of 20 intersect RS at D and E, with RD = 1, DE = 2.…

A: Given: ∠O intersect RS  at D and E in a △ROSwith the data  RD=1;   DE=2;…

Q: c. C = {re Q:r² ≥1} intC= bdC= dC = C is closed / open / neither closed nor open C is compact / not…

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Q: If y = sin 0 + 5, what is the minimum value of y? a) 4 b) 5 c) 3 d) 8 e) 11

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Q: 10) Prove the following. Use a 2-column proof, a paragraph proof or a flowchart proof. Given: V is…

A: Given V is the mid point of YWUY || XWwe have to prove that ∆UVY ≅∆XVW

Q: 1) Find the Centroid of a uniform piece of wood shaped as an "F" with respect to the bottom right…

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Q: can you answer  e) f)  g)

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Q: Prove that a torus at R³ is equivalent to the Cartesian product of two circles at R² 3 that is,…

A: Given Information:Torus: where  and  .Circle:  where .To show:The Torus at  is equivalent to the…

Q: 6. Let R to be the region bounded by y-axis, a curve y = 2², and a line y = L. (a) (**) Find a, b,…

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Q: In a quadrilateral PQRS, PQ = a. QR = b, SP = a - b. M is the midpoint of QR and X is a point on 4…

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Q: Lemma: Given AABC, let D E AB be such that A-B-D. Let ER be such that m/DAC < 0 <m/DBC. Then there…

A: According to the question,

Q: H-w lo Find the oliscontinnity point of &Cz) : ニ 5(2+i) 2+ci-2)Z -2i 근-3 S in Z

A: We have to solve given problem:

Q: Correct and detailed answer will be Upvoted else downvoted. Thank you! Let A and B be Jordan…

A: Let A and B be Jordan regions. Let A be a n dimensional rectangle and B be a m dimensional…

Q: Is Ź U Ź,asigma a lgebra over X? 4. Prove your an swer.

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Q: Question 2 a) Evaluate: b) s feta 00 +y² dxdy Show that for double integral dxdy rdrde

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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.