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 the line integral / (9x + 10y)dx + (5x – 6y)dy along the curve C : a = 6 cos t, y = 12 sint…
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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…
Q: Evaluate | (2x - y) dx + (x + 3y) dy. C: arc on y = x/2 from (0, 0) to (4, 32)
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…
Q: Evaluate (2х — у) dx + (х + 3у) dy. Jc C: arc on y = x>1² from (0, 0) to (4, 8)
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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
Q: Differentiate: y(x) along the curve xy =ex Show all working out.
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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…
Q: the detined b is Constant. Curiature a(t) =| 1 Cost, 1 sint, o of the curve d:laa)tR? where Find
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.…
Q: x = sin´t, y = cosʻt, 0<t<3™
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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- Determine dimension x to 3 decimal places.Ex) Consider flx)=x^2", x= 1.7,2.0, 2.3,2.6,2.9 P foruard diff. central diff Backuard difp. find f'(2.3) byThere are two tangent lines to the curve y %3D x+ 1 that are parallel to the line x - 2y = 2. Find either one of the them and put it in the form y = mx + b. Ente- the valu. | the ansver bov belew.
- Find the length of the curve 22 n. 4.-0) to the point (e. r. J -^²Find the center of the circle(s) tangent to 5x – 2y – 1 = 0 at (1, 2) with a radius of 3. Express your answer as ordered pairs with coordinates rounded to the thousandths place, i.e. (3.123, 4.567). The x-component of the center of one circle is (_ ). A The y-component of the center of one circle is (_ The x-component of the center of the other circle is (_. A The y-component of the center of the other circle is ( v Hide hint for Question 3 Here you get two equations and two unknowns, since we know the center is at some point (h,k) the distance between that point and the point on the circle (1,2) is (1-h)2 + (2-K)2 = 32 We also know that the line containing the center of the circle is perpendicular to the tangent line. Thus using what we know from equations of lines we, that line's equation is y = -2/5x + 12/5 This gives us 2 equations and two unknowns. Since the first equation is squared, we know that we will get two solutions (Verify by drawing the picture).obtain the dient to wilth Curve gra paramitvic eguation given by 8=ln2 and 3. sigh 2t when ヒz |
- 6. Trace the curve r? = 4cos*etan?e.Find the length of the curve x = 2 + 3t, y = cosh 3t, 0Sketch the curve y = 1/(1+e¯*). Logori+hmie lononontiel dlifforontiConstruct an OC Curve for N = 6000 , n = 82 and c = 3 using about 10 points, and also provide your calculated values in a tabular form. Plz do fast ASAPFind the solution to the differential equotion that Sotisies the quen inital condiionThe second derivative of curve: y = acosx, will be Select one: O -acosI acost -asinx asinzSEE MORE QUESTIONS
