3 9–? V1+x²+? dy dx dz O JO

Q: What is the slope of the line tangent to the polar curve r = ㅠ Ө - ? O 1 √√3 ✓ 2 T -||♡33 √√3 cos at…

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Q: Let (r, 0) denote the usual polar coordinates. Show that if U(r, 0) is a harmonic function, then so…

A: Given that  denotes the usual polar coordinates.We need to show that, if  is a harmonic function,…

Q: Q2: Sketch the polar function r = 6 cos 30 ,-n <0 < T

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Q: Consider the following. x = 3 cos(8), y = sec²(0), 0≤0 < 1/12 (a) Eliminate the parameter to find a…

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Q: How to solve this equation y'''+2y''+4y'+8y=5e^(3t)+1 using Method of Undetermined Coefficient

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Q: 3. Find the polar coordinates of all points on the cardioidsr=1- sine, at which there is a…

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Q: 4 16-y² •LIV (1 − g? _ g) dedy. 2. Use polar coordinates to evaluate

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Q: Compute sin z dz , where a is the piece of the parabola with equation y= a?, which lies between the…

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Q: Find the equation of the tangent plane to the graph of G(u, w) = cos (uw) at the point (2, 1). (Use…

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Q: Find the slope of the tangent line to the polar curve r = 4 - 3 cos (0) at 0= - T 3

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Q: Q5 By changing to polar coordinates, evaluate "S cos (x' + y° ) dxdy .

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Q: 3. find the of points P(x, y) whose sum of its distances from the two fixed points (4-2) and (-2,2)…

A: As you have mentioned I have to answer part 3 only. We have to find the equation of the locus of…

Q: Find the equation of the tangent to y-cos 2x at the point 0. Oal y--2- Ob) y- 2x+ O) y--+1 O d)…

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Q: Let (r) denote the usual polar coordinates. Show that if U(r, 0) is a harmonic function e. a…

A: A function is said to be harmonic function if it satisfies the Laplace equation. Now we only check…

Q: Determine the phase shift of the sinusoidal function y=-3 sim 2[(x − 3)] + ¹. +1. a) 2 rad to the…

A: Given that The sinusoidal function isy=-3sin[2(x-pi/3)]+1 ---------(1)We know that the general form…

Q: Find the slope of the tangent line to polar curve r = 6 sin 0 at the point 2 y = 1.5 + (a - 1.5/3…

A: Find the slope

Q: Eliminate the parameter for the given parametric equations to write an equation in the form of y=…

A: Given x=ln t and y=et

Q: √9-1² - Compute the following double integral LS sin(x²+y2) dy dx by converting to polar…

A: The given integral: ∫-33∫09-x2sinx2+y2 dydx

Q: Q2: Sketch the polar function r 3 6 cos 30 ,-n<0 < m

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Q: dy dy 2. Use the definition of the derivative dx and the product rule to find the de dy of the polar…

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Q: 9-y² 2. Evaluate the integral (2.x + y) dady by converting to polar 9-y? Coor- dinates.

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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.