The length of the polar curve r = e80/15, 0

Q: 3. What is the length of the curve r = cos3 (-) where 0 < 0 <: sos

A: See the attachment

Q: A natural cubic spline S on (0,2] is defined by Jsin - 1+2-r. S) = if Osr<l. |S,0) = 2+ b - 1) + cư…

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Q: Find the solutiTon of followina ordfnarg differentral equation -2x

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Q: 2.2 Prove that Te -dz < 3 ez z2 +7+1 where C is the arc of the circle |2| = 3 from z = 3i to z = -3.

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Q: 1. Use Green's theorem in order to compute the line integral $ (3cos + 6y?) dx + (sin(5") + 16x³) dy…

A: Here the given integral is                               ∮C3cosx+6y2dx + sin5y+16x3dy

Q: 3.4.8 Evaluate the area of the surface z = 2-x² - y² lying above the (x, y) plane. (Hint: Use polar…

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Q: Evaluate the spherical coordinate integral. 1- cos 2 2x x SS S p²sin dp do de 00 1- cos 2 2x x SS S…

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Q: The bounded solution of Laplace's equation Urr + =u, + ÷U90 =0 outside 3 which satisfies the…

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Q: 3. For what value of K the velocity field in plane polar coordinates given by v, = tion of…

A: 3. The given values are,vr=K36r2-1cosθ and vθ=k36r2+1sinθ

Q: Which one of the following is the parametric equa- tions of the line that is normal to the surface…

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Q: 4. Use Green's Theorem to evaluate the line integral | 2xydx+ xy'dy, where C is the triangle with…

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Q: Use Green's theorem to evaluate the integral $(sinx- dx+( +siny)dy where D is the annulus given by…

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Q: 1. Let C be a path along the upper half of a circle from the point P(2,0) to the point Q(-2,0).…

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Q: 3 Evaluate the integral cos(x² + y²)dydx by converting to polar coordinates 0 0

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Q: Let PQ be an h-line in a Poincare disc with center 0. a) The h-points A, B in PQ are located such…

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Q: 12. Consider the lamina covering the regon x442-2,0EXET WH aunsity functionplx,u) = - 5x + 2u+5. 1ts…

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Q: 2. Use polar coordinate to evaluate the integral cVa2-x2 dydx (1+x²+y²)2

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Q: 3.4.4 By transforming to polar coordinates, show that the double integral (x² + y²) ² dx dy (xy)²…

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Q: Use Green's theorem to evaluate the integral (sinx- dx+( +siny)dy where D is the annulus given by…

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Q: 2. Let R be the region inside the curve C :r=1+ cos 0 and to the right of the line l :r = 3 sec 0.…

A: To find point of intersection equate both r and find value of  θ which lie in the interval -π,π For…

Q: 2.2 Prove that e? dz] < 3 +++1 where C is the arc of the circle |2| = 3 from z = 3i to z = -3.

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Q: 1 Change the double integral J. dydx into polar integral. 4-x² x² + drde drd0 drde 2[-drde or

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Q: 7. (~Ch16 Review #6) Compute y3 dx + x² dy where C is the arc of the parabola x = 1- y² from (0, –…

A: In this question we need to find the given line integral .

Q: 3. Consider the ra greater across z =1-r² - y² plane and the s and a paramet

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Q: Q.1) Use the polar integral to evaluate 2 dydr 71+ Vr2 + y?

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Q: Find the temperature distribution in an insulated metals disc (say, a coin) of radius 1, whose…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Show that the general solution to the two-dimensional Laplace's Equation. et = 0 is (Acosh(tx)…

A: We have to show that the general solution to the two-dimensional Laplace's Equation…

Q: 3 Consider cune detined by y cos (T2) =UY +y+2 2 ) Verify point (2,-2) belongs to this curve, fond…

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Q: (10) Find the work done by F = -yi+ xj+ zk on a particle moving along the helix r(t) = where 0 < t <…

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Q: Which of the following is an arc-length parametrization of the line segment from (2,1) to (1,3)?…

A: We will find out the required value.

Q: 4. Calculate the arc length of the polar curve r = e38 from 0 = 0 to 0 = 2.

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Q: 1.13 Evaluate the line integral $ x*dx + xydx where C is the triangle with vertices at (0, 0), (0,…

A: The given function is x4dx+xydy By green's theorem, the integral becomes, ∫06∫06∂M∂y-∂N∂xdxdy where…

Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, —12t) (c) Determine the…

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Q: Q1: Consider the curve in E' parameterized by C:(t) = 1- Find the arc-length of the curve r(t)? 2-…

A: Given equation of the curve is rt=cos5t, sin5t, 12t

Q: 4. Use Green's Theorem to evaluate the line integral | 2xydx+ xy*dy, where C is the triangle with…

A: The given triangle C with the vertices (0,0),(1,0) and (1,2) is as as shown below.

Q: Show that the area of the surface of the solid generated by revolving the cardie r = a(1- cos 0)…

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Q: If the electric intensity in the vacuum E = Eocosθar - Eosinθaθ is the divergence of the electric…

A: In the question it is asked to calculate the curl of electric intensity given.

Q: By converting the integral 1-f dvdx into polar coordinates, the limits of integration of o are:…

A: The limit of x is from  -1 to 0. So, the theta can not be in the first and fourth quadrants. The…

Q: 1.Let 3 le the solid obtained by rotating by region shown in the fiqure about the Assume as3 and b=…

A: Given: y=ax(x-b)2 and y=0 and  0≤x≤b The rotation about the y-axis. Assume a=3 and b=1

Q: Suppose the divergence of the electric field in some spherical region is found to be V E = 5kr³.…

A: as given,   the divergence of electric field in some spherical region is ∇·E=5kr3 claim- to find the…

Q: 8. Set S be the bondary of the cube with side length 1 in Oc tant 1. Is in 6 pieces) Use Stokes…

A: (1) Over the surface ABCD ∫sx dy dz +z dz dx=∫01dz∫01xdy…

Q: The area of the closed region bounded by the polar graph of V3 + cos 0 is given by: Select one: O o…

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Q: From Rogawski ET 2e section 8.1, exercise 11. Approximate the arc length of the curve y = i x4 over…

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Q: Calculate the line integral f(-102 + 4z + 5) de + (-7z – Oy? – by – 4) dy, where Dis the annulus…

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Q: A curve is drawn on a sphere of radius "a' and the principal normal at a point P makes an angle 0…

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Q: Consider the double integralf dydx. By converting to polar coordinates, the limits of integration of…

A: Draw graph of circle  as per upper limit of y

Q: (9) Evaluate by converting to cylindrical polar coordinates 322dV where E is the solid bounded by y…

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Q: 1. Find parametrizations of the curve of intersection of x² + 4x + z² = 0 and x- – 2y + z = 3.

A: Given curve is x2 + 4x + z2 = 0 .  This can be written as (x+2)2 + z2  = 4  So the curve is a circle…

Q: The area of the rotational surface resulting from rotating the arc of the curve x=cos^3 t, y=sin^3 t…

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Q: Find ¹JJ²₁ z dV, where E is the solid tetrahedron with vertices (0,0,0), (3,0,0), (0,2,0), and…

A: The solid E is the tetrahedron with vertices 0, 0, 0, 3, 0,0, 0, 2,0 and 0, 0, 1. Draw the solid E:…

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.