O Identify all the ponts Crit) on Z=F(xcy)=cos (x+y) ot which tangent vecfors to Z=F(xcy) are paraliel to x and Shaw work and circle only y axes. the answer.

Q: Evaluate the iterated ntegral by Lonverting to polor coordinates. 2. zy dx dy 34

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Q: 77. Prove, in two ways, that the arc length of a linear function f(x) = mx + c on an interval [u, b]…

A: f(x)=mx+c on an interval [a,b] Note: we prove part a) only ,in part b) theorem 6.7 not given

Q: Find the points on the cardioid r = 1−cosθ at which there is a horizontal tangent line, a vertical…

A: Consider the given: r=1−cosθWrite the cartesian…

Q: Show that the volume of solid formed by revolving one loop of the curve r2 = a? cos20 about the line…

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Q: 2) usins Culcuulus for parametrre curres. Show trat the aren of a idis e of radius Ris siren by…

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Q: Let f(x,y)=x^3-cosy. Find the tangent plan for f(x,y) based at (1,pi).

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Q: Find the area outside "r^2=9cos(2theta)" and inside "r=2-cos(theta)"

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Q: Find the gardientoff at the indicatedpoint. frx,y)=D5sin x+Cos3y ;

A: Given: f(x,y)=5sinx2+cos3yπ2,0

Q: Q3 Point out the singularity and is ty pe of follo wing fune tions 22 () d) Sin t2 24

A: Singularity

Q: Express the arc length of the curve y = tan x for O < x < ~ as anintegral (but do not…

A: Given that, Curve, y=tanx 0<x<∞

Q: Find the arclength of y = sin (x) on the interval [0, a]. %3D

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Q: Use green's theorem to calculate the integral Fdr, F(r, y) = (e* + x²y , e³ – ry² + sen(3) + 2)…

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Q: O show mat me Nomal point @ X= a( Coro +o Smo) y= a(8in0-o Cor0) dy Sine %3D ep" of Normal S-ゴ」=…

A: the parametric function is x=a(cosθ+θsinθ) y=asinθ-θcosθ Differentiate each with respect to theta…

Q: Evaluate the line integral L(r – y*)dx + (1+ y² + =*)dy, where Cis the circle of radius 2 centered…

A: We have to evaluate the value of the integral

Q: x = r², y = (0 <1 < 1)

A: For x=x(t), y=y(t), a≤t≤b Arc length formula is L=∫abdxdt2+dydt2 dt

Q: Compute the arclength of the curve in the plane given by C = {(r, y) = (t² cos(t), t² sin(t)) for 0…

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Q: Suppose F(x,y)=4yi +3xyj. Use Green's Theorem to calculate the circulation of F around the perimeter…

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Q: Find the arc length of f(x) = () (x² + 2)z on the interval [0,9] %3D

A: (6) Given function is fx=13x2+232 and interval is 0,9. We have to find the arc length of fx=13x2+232…

Q: Use Green's Theorem to evaluate F. · dr, where F = (Va + 4y, 2x + and C consists of the arc of the…

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Q: Find the anea of the vegion in quadrant Ps bou nodod ist 4 the conie the by the right by the line…

A: Given curves, y=ex+12,y=e-x+12,x=2 ln2 To find the area of region bounded by these curves.

Q: Find the arclength of r(t)= on the interval from t equals zero tot equals 2 times pi.

A: Given:  r(t)=&lt;5cot(t), 3 sin(t), 4 sin(t)&gt;To find:  Arc length form t=0 to t=2π

Q: Find the tungent Irne of where C: F) = is parallel to xy- plane

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Q: Consider a new curve Č parametrized by r(t) = (cos t esint, sin t- cos t), 0 <t <I but with F still…

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Q: Find the sum of the residues of f (z) = sin z at its poles inside the circle |z| = 2. z cos z

A: Residue theorem∮f(z)dz=2πi(R1+R2+.........Rn)             =2πi(sum of the residues at the poles…

Q: The integral that represents the arc length of the curve y = Inx from the point (e, 4) to the point…

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Q: USE THE METHOD OF VARIATIOH Of PARAME TERS To SOLUE THE FOLLOWIHG DIFFEREHTIAL EQUA TION!…

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Q: Find the speed of the cycloid c(t) = (4t − 4 sin t, 4 − 4 cost) atpoints where the tangent line is…

A: Given: c(t)=4t-4sin(t), 4-4cos(t)

Q: Let C be the arc of the circle |z| = 2 from z = 2 to z = 2i that lies in the first quadrant. Without…

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Q: Compute the arc length function L = | ||r(u)||du for r(t) = (16t/2, In(t), 32t), and a = 1. %3D la L…

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Q: Set up the definite integral(s) equal to the arc length of the curved defined by the parametric…

A: Use the formula of arc length in parametric form and simplify.

Q: Which of the following represents the arc length of the vector function r(t) = (sin 2t, e, ) on the…

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Q: Consider the parametric curve: x = 5t² y = 2et Which integral gives the arc length of the curve over…

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Q: to find 2y dx-xdy, Use where C is the green's theorem the the eircle wi'th radivs 4 Centered at…

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Q: If a(s) is a curve parametrized by arc length, prove that a"(s) is per- pendicular to a'(s). (ii)…

A: Given the curve

Q: Use Simpson’s Rule with n = 10 to approximate the length of arc of r(t) = t i + t2j + t3k from the…

A: Given,

Q: Consider the part of the helix ~x(t) = (2 cost, 2 sin t, 3t) that is bounded by t = 0 and t = 2π.…

A: We have to find the arc length of above helix

Q: Let f(x)= /Ve' – 1 dt . Determine the arc length of y=f(x) from =0 to =2. Round your answer to two…

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Q: Approximate the arc length of the curve y = x over the interval [1, 2] using the trapezoidal rule…

A: Given y=14x4 in [1,2] , 7 sub intervals  y'=14×4x3 = x3 Area length = ∫ab1+y'2dx…

Q: Is it true that Arg(z) = arctan for x + 0, where x = Re(z) and y = Im (z) ?

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Q: Evaluate the following line integral. xy ds; C is the portion of the unit circle r(s) = (cos s, sin…

A: Here we have to evaluate the following line integral,  I=∫Cxyds; C is the portion of the unit circle…

Q: Evaluate the line integral L(a - )da + (1 + y° + æ")dy, where Cis the circle of radius 2 centered at…

A: We have to evaluate the integral.

Q: C is the part of the circle = 1 in the first quadrant, find the following line integral with respect…

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Q: Evaluate the line integral ſc(4y+ tan? x)dx + (6x – evsin´y)dy over curve C that is the circle x2 +…

A: Green's theorem problem....

Q: Find the value of a such that the arc length of the catenary y = cosh x for −a ≤ x ≤ a equals 10.

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Q: Find the arc length over the domain 0<t<5 7t 1 10) x= V-7t – 2, y=- + | 4 2

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Q: Compute the arc length function L = | ||r(u)||du for r(t) = (16t1/2, In(t), 32t), and a = 1. %3D %3D…

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Q: Use Green's Theorem to evaluate F. dr, C where F = (Va + 6y, 4x + /ỹ C consists of the arc of the…

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Q: Find the arc length of the curve Cycloid arch: x = a(θ − sin θ), y = a(1 − cos θ) , on the interval…

A: Cycloid arch: x = a(θ − sin θ), y = a(1 − cos θ)  interval [0, 2 ].