Q: If y = Vx(3 – x)², show that- dy (3-х) (3-4x) Find the x coordinates of %3D dx all points on y =…
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Q: Evaluate (2x – y) dx + (x + 3y) dy. C: arc on y = x312 from (0, 0) to (4, 8)
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Q: 23. Evaluate Jcxy dx + (x + y) dy along the curve y = x² from (-1, 1) to (2, 4).
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Q: Evaluate the line integral (8x + 7y)dx + (2x - 7y)dy along the curve C: a = 8 cos t, y = 16 sin t (0…
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Q: Find the curve y(x) that minimizes the I Cy) = S. cos x)+ ]2 Cunc tonal %3D
A: solution:-Given I=∫1+cosx+y121/2using Euler's equation ∂f∂y-ddx∂f∂y'=0sincef=1+cosx+y121/2is…
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A: Follow the procedure given below.
Q: Evaluate [12x. (2x - y) dx + (x + 3y) dy. C: arc on y = x/2 from (0, 0) to (4, 32)
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Q: b) Evaluate S(2y + 4z)dx + (2æ + 3z)dy + (4x + 3y)dz, where C is the curve given by r(t) = for 0 <t…
A: given ∫C2y+4zdx+2x+3zdy+4x+3ydz where C is the curve given by rt=t3,2sinπt2,3cosπt2 for 0≤t≤1…
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Q: find both dy/dx (treating y as a differentiablefunction of x) and dx/dy (treating x as a…
A: Differentiating with respect to x, we get
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Q: Consider the curve defined by xy + y2 = 21 Determine dy/dx for this curve at the point (4, 3)
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Q: Differentiate: y = /16 – z² – 4 arccos() e+4 y' = Oy= Oy- %3D
A: Given that : y = √(16 - x2) - 4arccos(x/4). We find derivative of this function (y). Here i…
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A: We are given : α(t)=1rcos t,1rsin t,0 ⇒α'(t)=-1rsin t,1rcos t,0 Now, the Unit tangent Vector is :…
Q: Evaluate 112x C: arc on y = x5/2 from (0, 0) to (4, 32) (2x - y) dx + (x + 3y) dy.
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Q: dy (5) Obtain the integral curve for +y cotx dx = e*cscx passing through the point (0, 0).
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Q: Evaluate (2x - y) dx + (x + 3y) dy. C: arc on y = x/2 from (0, 0) to (4, 8)
A: Here we have to evaluate ∫c (2x-y)dx+(x+3y)dy
Q: Evaluate the line integral / (7x + 5y)dx + (3x – 9y)dy along the - curve C: x =2 cos t, y = 4 sin t…
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Q: Evaluate S (2x - y) dx + (x + 3y) dy. C: arc on y = x5/2 from (0, 0) to (4, 32)
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Q: Consider the curve parametrized by x www = 1 + ln(t) and y = t¹ + 2t. dy a) First eliminate the…
A: topic - derivatives
Q: A. Use Simpson's rule to evaluate -dx ,by taking n= 4. Inx B. Find the length of the curve y = x…
A: Answer
Q: Evaluate the line integral curve C: x = = 4 cost, y (5x + 7y)dx + (3x − 6y)dy along the = 8 sint (0…
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Q: Evaluate the line integral / (3x + 9y)dx + (4x – 5y)dy along the curve C : x = 10 cos t, y = 20 sin…
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Q: dw by using Chain Rule. (Your answer should not include z ond y. dt = z+v? z = cost + sin t and y=…
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Q: Find the value of Jsinydx+ (xcosy-siny)dy, where Cis any curve from (2,0) to (1,n). Ca.2 Cb1 none of…
A: Green's theorem: ∫C Pdx+Qdy =∬D ∂Q∂x-∂P∂y dA where P and Q have continuous first order partial…
Q: find both dy/dx (treating y as a differentiablefunction of x) and dx/dy (treating x as a…
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Q: Evaluate (2x - y) dx + (x + 3y) dy. C: arc on y = x12 from (0, 0) to (4, 8) 528/5
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Q: 5. Find the length of the curve given by y= Vt* – 1 dt and 1<x<2.
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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: where t is a non-zero parameter. Show that dx 28 Given that x=z and y==. 1+r Hence find its value at…
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Q: Find dy/dx and d²y/dx². x = et, y = te¬t dy dx dzy dx2 For which values of t is the curve concave…
A: We have to find derivative
Q: Evaluate the line integral (5x + 8y)dx + (3x – 5y)dy along the - curve C : x = 10 cos t, y = 20 sin…
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Q: Find dy/dx in terms of x and y if arctan(x*y) = y“. dy dr
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Q: Evaluate the line integral curve C′ : x = 4 cost, y = 8 sint (0 ≤t≤7) NOTE: Enter the exact answer.…
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Q: A particular curve has unit binormal b - sin t, cos t, 2), unit normal n (- cost, - sin t, 0) and =…
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Q: Find the length of the curve y = ln (sec x), 0 <I<÷.
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Q: Q1: Use Green's theorem to evalute S. (xy + y2)dx+ x?dy by the curve y = x and y = x2.
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Q: Evaluate the line integral / (3x + 7y)dx + (2x – 3y)dy along the curve C: x = 6 cos t, y 12 sin t…
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Q: Find equations for the a) tangent line and b) normal plane to the curve 1 x=t- cost, y = 3+ sin 2t,…
A: x=t-cost, y=3+sin2t, z=1+cos3t We know that rt=xt, yt, zt dxdt=1+sint, dydt=2cos2t, dzdt=-3sin3t At…
Q: Evaluate ſxy dx+(x+y)dy along the curve y=x² from (−1,1) to (2,4).
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Q: Compute 2z dz (2² – i)3 when y is any arc z = z(t) in C with |z(t)| > 2 for every t, with…
A: Let the required arc be ABC, which starts at z=3 and ends at z=2i: The shaded area shows a sector…
Q: Q1-If x= cot- VE, y =, find 2 dy dy dx'dx at t = 2. t+1
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Q: A particle is moving along the curve y=x- 2 where x and y are functions of t. Find dx/dt if dy/dt =…
A: From the given problem: y2=x3-2 ....(1)dydt=4. Now differentiate the function with respect to x.…
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A: Given x=sin2t, y=cos2t, 0≤t≤3π
Q: . Find SF dř where F(x,y,z) = (3y?e*, 6ye* -, 1+) and C is the curve F(t) = (sin t, ,2-) for 0 stsn.
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Q: Evaluate the line integral / (4x + 8y)d.x + (4x – 9y)dy along the curve C : x = 10 cos t, y = 20…
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Q: Evaluate (2x - y) dx + (x + 3y) dy. C: arc on y = x3/2 from (0, 0) to (4, 8)
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Q: Integrate to find the length of the curve. 8 S = 2 - + 4t dt 4 + 8 2t ++) dt = (? +t ln(t) 1 II
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Obtain the second derivative as,
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- name another different type of 3-D curve from vector valued functions so far I have 1. linear 2. quadratic 3. cubic 4. sinusoidal 5. ?????Find the curve through the origin in thexy-plane which satisfies y''=2y' and whose tangentat the origin has slope 1.Find a parametrization for the curve described below. The line segment with endpoints (-2,4) and (0,5). X = ----- for 0 ≤ t ≤ 1
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