Given the function f(r, y) = 2y, find two distinct regions R1 and R2 such that SS s(7, y) dA = [[ s(1, y) dA R1 R2 Show your work on finding these regions and that both definite integrals are equal when you find them. Hint: Notice that f(x, y) only depends on y.

Q: Q5: A) Evaluate the following integral : S(z? – z-2)² + 4 dz B) Find the slope of the line tangent…

A: To evaluate the integral, the function z2-z-22+4 has to be first simplified. Now, z-2 can be…

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Q: Given the function, x = 3 + Vx? + y² , find y. Vx² +y² - X y Vx² + y? - > ア= y Vx? + y² + x ア= y Vx?…

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Q: 1srs0, then (i) Test whether the Rolle's theorem holds for the function f(x)=D< In 0<xsl the…

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Q: 3x + 5x #2. R(x)= 일 때 R'(0)을 %3D 1+3x° + 6x° + 9x°

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Q: Q6. Let w = f(r,0), r = √x' + y³, 0 = tan'(y/x), ), find aw ?х > and ди ду in terms of r and 0.

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Q: For g(x, y) = sin'(x² + y? – 12) the domain of the function is the area between two circles. Show…

A: Please see the explanation below

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Q: For the function f(x, y) = (cos x)ey +v 1 + x + y. %3D Show the process of using the linearization…

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Q: Solve for Txyz given the function T(x, y, z) = z tan (In x - √y)

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Q: To calculate the surface area of a sphere of radius R we can use the formula b. S= 27 f(x)\/1+…

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Q: Let f(x, y, z): = x² - tany² 2xyz Solve for fry

A: Given :fx,y,z=x2-tany22xyz To find fzxy

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A: Simply  Apply the formula P=R-C Then diffrentiat this equation with respect to x Finally we got…

Q: Let f(x,y) = x³y? The third derivative fexy

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

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Q: Given f(x, y) = sin(x + y) where x = sºt5, y = 6s – 5t. Find

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Q: Q1: Find and : for the function f(x,z) %3!

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: Following function be f(x,y) = x2 + y2, with x(s, t) = (s + 1) / t and y = (t2 + 1) / s. Determine…

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Q: Estimate the amount of change in f (x, y,z)= cos (7xy)+xz² if the point P(x,y,z) moves a distance of…

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A: The given function is: f(x)=sin x To find the linear approximation of it close to 0.

Q: (등공) of and ôf Evaluate for f (x,y) = sin (3 x- 2y) at 36

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Q: Use a tangent plane to approximate the value of the following function at the point…

A: If the function is fx,y=arctanxy2-699 So, fxx,y=y21+xy2-6992fyx,y=2xy1+xy2-6992 Now,…

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.