tiryent liae is hovizontul ov verlical Y=rsine = ed sind te(-sime) al -sine) y'= e@ gino tea Ceso) eo(sretose) =c %3D ea Ccoso sro)=0 nori zontad tengent when verical tngent ea when dx =o e (uresi) Find the points on the given curve where the tangent line is horizontal or vertical. (Assume 0 < e < 2n. Enter your answers as a comma-separated list of ordered pairs.) r= e0 horizontal tangent (r, e) = vertical tangent (r, 8) =

Q: x² cos²y – sin y = 0, (0, ) re (a) tangent and (b) normal to the curve at the given

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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: 2. Let y be the curve in R° given by t (t, 2 cos t, 2 sin t) for 0 < t< 47. Compute y? ds

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Q: 1. Find the length of the curve given by e' (sin t+cos t) , yY = e'(cos t – sin t), x = 1<t< 4 .

A: The length of a parametric curve is given by L=∫abx't2+y't2dt Now, we have…

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: 3 Z Eii %3D From the properties of characteristic equation of strain Zɛ, -Mw -Mw

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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: Find the length of the curve. r(t) = cos(2t) i + sin(2t) j + 2 ln cos t k,     0 ≤ t ≤ π/4

A: Consider the length of the curve is, r(t)=costi+sintj+(lncost)k Then,…

Q: Find equations for the tangent and normal to the cissoid of Diocles y2(2 - x) = x3 at (1, 1).

A: Find dy/dx using the given equation.

Q: 1. Find the moment of inertia, with respect to the line x=1, of the area enclosed by the loop of the…

A: Given: Curve y2=x2(1-x)----(i)

Q: bas S s 101 ub oteuleva (d) TOt J8 ei Jed TV=( lo moitesiesnil odi baid Find the equations of the…

A: The given function is y=1+4sinx at x=0

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: 1. Evaluate xyz dz, where C is the curve 7(t) =t cos(t)î + sin(t)ĵ – cos(t)k, 0 < t <1.

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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 S (2x - y) dx + (x + 3y) dy. C: arc on y = x5/2 from (0, 0) to (4, 32)

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Q: The value of cosh(3z+1)dz, where C is the line segment from z=1 C to z= 2i. O a. (-sinh(6i+1)+sinh…

A: We have to find the value of integral,  I = ∮Ccosh(3z+1)dz  ;  where C is the line segment from z=1…

Q: A particular curve has unit tangent u= (-2 sin t, 2 cos t, 3) and unit normal n (-cost,- sin t,0).…

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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: A) Find the distance traveled by a particle with position (x, y) as t varies in the given time…

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Q: 2. Find the length of the curve: y = 2 In (sin (x)):sxS*

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Q: Find the length of the curve x=1+2sin at, y=3–2 cos at, 0<t<l

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Q: Let C be the curve consisting of line segments from (0, 0) to (1, 1) to (0, 1) and back to (0, 0).…

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Q: Prove that the segment of the normal to the curve x = 2a sint +a sint cos't, y = -a cos't contained…

A: First find derivative then equation of normal line ,and point of coordinate axes and then use…

Q: Integrate f(x,y) =x -y over the curve C: x² + y = 16 in the first quadrant from (0,4) to (V8,18 - y)…

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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: bet PCa) + X"= 3x twen fca) %3D 3 dne equation of due tangent line to fcxD=(x'+2zx>Cx+x?+!_ y=2X df…

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Q: The integrating factor of the equation sec? y + xtany= x° is: dy de In|sina| O None of these…

A: We have to find I.F

Q: Find the arclength of the curve y = x – In x if < y< -1. Do not simplify your answer for this…

A: Given: y=18x2−ln⁡x if 18≤y≤e28−1 ⇒f(x)=18x2−ln⁡x if 1≤x≤e The arc length of the portion of the graph…

Q: 1. Find the length of the curve r(t) = (sin 2t, cos 2t) from t 0 to t= 2n. CoS %3D

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

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: Find the required x-value. For a x2-cu -curve with 27 degrees of freedom, find the X-value having…

A: Given data:Degree of freedom  =27 Area to the right  = 0.01

Q: - arctan(e**) dx =? 1+e2kx A) (arctan(e*)In [cos(arctan(e*)| + S In [cos(arctan(e*)da]+ c kekz B)…

A: Let I=∫tan-1ekx1+e2kxdx where tan-1ekx=arctanekx Put tan-1ekx=t…

Q: 4. Find the arc length of the curve x=y+y from y-1 to y-4

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Q: If a = 5+ti and y = 3t - t then dy at t = 1 dz is :

A: as per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: A curve has parametric equations x = 2 sin t ,y = cos (2t) + 2 sin t for −π/2≤ t ≤−π/2 . Find out…

A: Given : parametric equations x = 2 sin t , y = cos (2t) + 2 sin t for −π/2 ≤ t ≤ π/2     Note :…

Q: Starting from the point (2, –1, 2), reparametrize the curve r(t) = (2 – 2t, -1+ 2t, 2 – 3t) in terms…

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Q: Der. 2D 11 Find dy/dx and d2y/dx2. For which values of is the curve concave upward?

A: Given: x=t2+1 y=t2+t Differentiating x with respect to t, dxdt=2t Differentiating y with respect…

Q: cos(u) dx. int_ccC [2x*cos(y) \ dx \ - | x^2 sin(y) \ dy] x? sin(u) dul if C is the curve x^4+y^4=1,…

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Q: expardantial from the folloming data: Fit an of the type y= He curve 2 4 10 30 Erstimate the valve…

A: We can solve this using formula y= Aebx

Q: S(cscz cot z + 8z")dz O secz +z +c sec z+z+c O - sinz +z +c O cscz + z +c - csc z +z° +c

A: We will integrate the given function by using the formula of basic integrable functions.

Q: Find the distance traveled by a particle with position (x, y) as tvaries in the given time interval.…

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Q: What is the area of one of the petals of the rose curve r = 2 cos(20)? T/4 cos (20) d0 8. cos (20)…

A: We have to find

Q: 20 The arc length of the curve y = In(1-x²) for 0 sxs is 29 400 + 841 49 + In 34 + In 15 20 29 20 49…

A: The arc length of the curve y = In(1-x2) for 0≤x≤20/29 To select correct option

Q: Starting from the point (-3, –1, 1) reparametrize the curve r (t) = (-3+ 3t) i+(-1+2t)j+ (1+ 3t) k…

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Q: Show that the curve x = 3 cos(t), y = 2 sin(t) cos(t) has two tangents at (0, 0) and find their…

A: on solving this we get

Q: 3. Find S. F · dr where F(x,y, z) = (3y²e*, 6ye* F(t) = (sin t, ,2-) for 0 <tsn. 1+3) and C is the…

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