Q: Let y be the curve with vector form r(t) = (1/(t+ 2), sin(sin(sin t)), e-"). a) Determine whether…
A: The parametric curve is r(t)=⟨1t+2, sin( sin( sin t)),e-t⟩. x(t)=1t+2, y(t)=sin( sin( sin t)),…
Q: Find an equation of the tangent plane to the surface g(x, y) = x2 + y2, at the given point (1, −1,…
A: We have given the surface; g(x, y) = x2 + y2 and the point (1, −1, 2)
Q: 3) Find the exact length of the curve: x = y = In(1+t); 0<t<2.
A:
Q: Let C be the curve y = 2 ln(4 – x²), for – 0.3 < x < 0.8. A graph of y follows. - 2.79 2.76- 2.73…
A: Given: Here, y'=2ln4-x2' =2ln4-x2' =2·14-x2-2x =-4x4-x2
Q: 1. If the parametric curve $x=f(t), y=g(t)$ satisfies $g^{\prime}(1)=0,$ then it has a horizontal…
A: TRUE Slope of the curve, when in parametric form = dy/dx = g'(t) / f'(t)
Q: Use the IVT to prove that the curves y = x2 and y = cos x intersect.
A:
Q: Find an equation of the tangent plane to the surface at the given point. z = x2 - 2xy + y2, (2, 3,…
A:
Q: find the work done by F in moving a particle once counterclockwise around the given curve. F = (4x -…
A:
Q: 8. Show that the one parameter family of curves y² = 4k(k + x) (k E R) are self orthog- onal.
A:
Q: (5xy --- 6x(2^
A: Given, F=(5xy-6x2)i+(2y-4x)j and y=x3 from the point (1, 1) to (2, 8).
Q: A possible way for the parameterization of the curve C corresponds to: (9t – t² A) r(t) = , t, z(t)…
A: In the three dimensional system, a parameter(usually "t") is used to describe the variables x, y and…
Q: Let C be a portion of a curve from (2,0) to (2,2). Let F(r,y) = (tan(x²) + e²v¸ 2re²v
A: Introduction: A vector field is conservative if ∂P∂y=∂Q∂x, Where f(x,y)=Pi+Qj.
Q: Find an equation of the tangent plane to the surface at the given point z= 5x - xy3+y2, (1,1,5)
A:
Q: If C is a piecewise smooth curve from (1,2, 3) to (4,5,6), then | . dx + 2 dy + 3 dz=
A: The value of the given function can be found with the help of the integration. Substitution of…
Q: 1. Consider the implicitly defined curve Py- 2r = 25. (a) Verify that the point (1,3) is on the…
A: Given, x2y3-2x4=25
Q: 1. Show that the curve a(t) = (t,t² + 1, t – 1) is regular.
A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…
Q: 5. True or False: suppose that for any simple, closed curve C, ſF · dr = 0 where F(x, y) = (f(x, y),…
A:
Q: 7. Let F(x, y, z) = (2x, k + e¯²,-ye¬²) and C be the curve given by r(t) = (t, –t,3 – 2t – t2), t e…
A:
Q: = Let Co be the curve formed by the intersection of the surfaces x₁ = 2x² and X3 3x1x2, and let C be…
A:
Q: Find an equation of the tangent plane to the given surface at the specified point. z = In(x - 3y),…
A: Here, the surface is: z=ln(x-3y) To find the equation of the tangent plane at the point (7,2,0).…
Q: Prove that the following curves are intersecting with a right angle: 5y-2x+ y -x²y =0 2y+5x+ x* –…
A:
Q: 1. Sketch each curve in the z-plane, and sketch its image under w = 2². (a) |z1|=1 (b) x = 1 (e) y²…
A: We are authorized to answer three subparts at a time since you have not mentioned which part you are…
Q: Consider a particle moving rectilinearly according to x = 13 - 312 -45t m, where t is in sec. Draw…
A:
Q: Find T, N, and k for the space curve r(t) = - ti - (a cosh (t/a))j, a > 0.
A: Unit Tangent. Unit Normal. Curvature.
Q: Verify Stoke's Theorem for F =( x²)i +(xz)j + (xyz)k and C is the curve of intersection between z=1…
A: Given: F =( x²)i +(xz)j + (xyz)k and C is the curve of intersection between z=1 and z² = x² + y².
Q: 1. Let y be the part of the curve y =r² running from (-1,1) to (2,4). Calculate ry dr + (x+ y) dy.
A:
Q: F(x, y) = 2xyi + (y² – x²)j (x2 + y2)2 and C is any positively oriented simple closed curve that…
A: Given F(x,y) = 2xyx2+y22i+y2-x2x2+y22j To Evaluate ∫CF(x,y)dr
Q: (3)If F = (x points (2,1,1) ² yz, xyz² , zy² ). Find curl curl F at
A:
Q: Let C be the curve y = x³ – 3x2 + 4x – 1 joining the points (1, 1) and (2, 3). Find the value of…
A: We need to find value of integral.
Q: Let F= 3xyi + 2x² j and suppose C is the oriente curve shown in Figure 28. Evaluate F.ds both…
A: The line integral ∫CF·ds involves the integration over a specific path. In general surface,…
Q: (5) Determine whether Fř is independent of the path when C is any closed curve and (i) F(x, y, z) =…
A: Here we use the curl of vector function to determine its dependency on the closed curve as follows
Q: 2. Find an equation for the plane tangent to the surface 3x2 - 4xy+ z2 = 0 at the point (1, 1, 1).…
A:
Q: Let C be the curve y = 2/r for 1.3 <x < 3.2.
A: Given that: y=2x
Q: Let C: [o,2]> R be a curve defined by C(t) = (t²,t'). Evaluate. Sy dx x dy.
A: Given: C: [0, 2]→ℝ2 is a curve defined by C(t)=(t2, t3)implies x=t2 and…
Q: Find the tangent plane for the level surface f(x,y,z) = 7x5 + cos (5y) + In (9z) = c at the point…
A: Answer: In oerder to use gradients we introduce a new variable c= 7x5+cos(5y)+ln(9z) Therefore the…
Q: Let c be a smooth curve defined by r(t)= with 1
A:
Q: 1. Compute (1/zy, 1/(z + y))- dr along the curve (t, t2). 1<ts4
A:
Q: Use Green's theorem to evaluate S,(5xy + x² + y²) dx + (x² – y)dy where C is a closed curve that is…
A: The posted question has multiple questions but according to guidelines we will solve the first…
Q: If L is the tangent line to the curve 7 (t)= (2t-1, t, t-2) at (3, 4, 2) and the point where L…
A:
Q: Let a, b > 0. Show that S = {(x, y) E [a, 00) x R| - = 1} is a smooth curve.
A:
Q: 3) Find the divergence and curl of f3xi+ 5x} j + 2y²k, at the point (1,2,3)
A: Solution is done in step 2
Q: Find that F = 12x²yi + (4x + 8yz²)j + 8y² zk is conservative, and find a function f such that F =…
A:
Q: Show that the curve r(t) = ( t3 /4 - 2)i +(4/t-3)j+cos(t-2)k is tangent to the surface x3 + y3 + z3…
A:
Q: Find the diffrential equation of for each of the curves determined by the condition that at each…
A: length of subtangent =ydydx
Q: Find an equation of the tangent plane to the surface z = √(x2 + y2), at the given point (3, 4, 5).
A: We have given equation z=x2+y2 First we rearrange the equation of the surface into the form fx,y,z=0…
Q: 3) Find the exact length of the curve y = x² – In x for 1< x < 2. 1„2
A:
Q: (1) Find the curl of the curve F=(x*y.y*z.2x) (0.0. y+1) (-x'.2'.y+1) b) d)
A: We have to find the curl of the curve F=(x2y,y2z,z2x) curl is defined as the cross product of ∇ with…
Q: 3. Find the equation of the tangent plane to the surface in R³ defined by z = 2x² + y² at the point…
A:
Q: Find an equation of the tangent plane to the surface at the given point. - . z = 8 —х — у, 3 (3, –4,…
A: Given plane is z=8−83x−y. We have to find the equation of tangent plane to the surface at the point…
provide detailed/complete solution. thank you for the help
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
- Let c be a smooth curve defined by r(t)= with 1compute ∫C F · dr for the oriented curve specified. F(x, y) = (ey^-x, e2x), piecewise linear path from (1, 1) to (2, 2) to (0, 2).Consider the parametric curve segment (t, t2), t ∈ [0, 1]. What is the firstorder derivative of the curve at t = 0? Show that exactly the same curve segment can be re-parameterized so that the first-order derivative at t = 0 is different.
- Let a, b > 0. Show that S = {(x, y) ∈ [a,∞) × R |x2a2 −y2b2 = 1} is a smooth curveFind the points on the curve x2 + xy + y2 = 1 in the xy-plane that are nearest to and farthest from the origin.1. If the parametric curve $x=f(t), y=g(t)$ satisfies $g^{\prime}(1)=0,$ then it has a horizontal tangent when $t=1$
- Find the diffrential equation of for each of the curves determined by the condition that ateach point (x, y) where the length of the subtangent is equal to the sum of its coordinates.Find an equation of the tangent plane to the surface z = √(x2 + y2), at the given point (3, 4, 5).Suppose that a parametric curve is given by x = f(t), y = g(t) for 0 ≤ t ≤ 1. If f 0 (t) > 0, explain why we may express the curve as the graph of a function y = h(x) for some function h(x).
- Evaluate∮C (x + 3y)dx + ydy where C is the Jordan curve given by thegraphs of y = e^x, y = e^−x and the horizontal line y = e^−1a) By Green’s theoremb) By direct computationUse Green's theorem to find the k number that satisfies (k + 3) ∫C((k/2)*(x^k)*(y^2))dx + ((yx^(k + 1)) + y^2) dy = 7680, where curve C is given below.Show that the curve = Vti + vt + (2t - 1) k is tangent to the surface x² + y2 -z = 1 when t = 1