Find the work done by F over the curve in the direction of increasing t. F= 11zi + 11xj + 11yk, r(t) = ( sin t)i + (cos t)j + tk, 0sts2n .....

Q: Find the work done by F over the curve C in the direction of increasing t,where F =-5 vi +5xi+8z’k…

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Q: find the work done by F over the curve in thedirection of increasing t. F = 6z i + y2j + 12x kr(t) =…

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Q: Determine the open t-intervals on which the curve is concave downward or concave upward.  x = 4 cos…

A: given,             x = 4 cos t, y = 2 sin t, 0 < t < 2∏

Q: Find the work done by F over the curve in the direction of increasing t. F = -7y i + 7x j + 9z 7 k;…

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Q: et C be a portion of a curve from (2,0) to (2,2). Let F(r, y) = (tan(2?) +2, ) Is F conservative?…

A: In the given question, the concept of integration is applied. Integration Integration is a method of…

Q: compute f ds for the curve specified. f(x, y) = /T+9xy, y=x³ for 0 < x < 1

A: Line integral: If rt=x(t), y(t), a≤t≤b then, ∫Cf(x, y)ds=∫abfx(t), y(t)x'(t)2+y'(t)2dt

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Q: Find an equation for the tangent plane to the function f (x, y) = Jy – x at (1,2,1). %3D

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Q: Determine the length of the curve (a) F(t) = (cos t, sin*t, 2) on the interval 0<t< %3D (b) F(t) =…

A: Length of curve is given : L = integration (r'(t)dt) from a to b.

Q: find the work done by F over the curve in the direction of increasing t. F = xy i + y j - yz k r(t)…

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Q: Find the work done by F = - 2zi + 7xj + 5yk over the curve C in the direction of increasing t. C:…

A: Solution of this question is

Q: The parametric form of the tangent line to the image of f(t) = (4t2, ,t+ 4) at t = 1is L(t) =

A: First we will find the tangent vector by differentiating f

Q: Find an equation of the tangent plane to the graph of F(r, s) at t F(r. s). - (3r4 1 + 1), (-1, 1.…

A: Introduction: Let z=f(x,y) denote the equation of a surface S in R3, and P=(a,b,c) denotes a point…

Q: find the work done by F over the curve in thedirection of increasing t. F = 2y i + 3x j + (x +…

A: To find the work done by F over the curve in thedirection of increasing t. F=2y i+3x j+(x+y)…

Q: (2) Find the work done by F over the curve C in the direction of increasing t. Explain why the sign…

A: Question: Calculate the work done by  Fx,y,z=zi^+xj^+yk^ over the curve  C : r¯t=sinti^+costj^+tk^ ,…

Q: The curves C,:x=t, y=t, z=t, t20 and C,: x= sint, y 1+cost, z=1, 120 have intersection at the point…

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Q: find the work done by F over the curve in thedirection of increasing t. F = z i + x j + y kr(t) =…

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Q: Find the tangent to y = cos x at x = 5- O A. y=x+7 O B. y= -x+7 O C. y= -x-7 O D. y= 1

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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: Use Green's Theorem to evaluate | F. dř, where F = (Va + 4y, 2x + 9) C consists of the arc of the…

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Q: Let H(x) = S V1+t² dt. Find the equation of the tangent line to the curve y = H(x) at x = 0. ex

A: It is given that, H(x)=∫ex11+t2dt we have to find the equation of tangent line on curve y=H(x) at…

Q: compute the length of the curve over the given interval.  r(t) = (cost,sin t,t3/2), 0 ≤ t ≤ 2π

A: Derivative of a function is represented as the change in variable with respect to change in another…

Q: 3. Use the Fun.Theorem to evaluate F dr, where F = 3xy?ī+ 3x*yj , πί and C is the curve described by…

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Q: Use Green's Theorem to evaluate F. dr, where F C consists of the arc of the curve y 1x x2 - from…

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Q: find the work done by F over the curve in thedirection of increasing t. F = 2y i + 3x j + (x +…

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Q: 7. Consider the function f: R → R³ given by: t+1 f(t) = sin(cos(t)), tet) t2 +4° Find f'(t) for all…

A: The derivative of the function is the measure of how fast the function is varying with respect to…

Q: Use a local linear approximation of the function f(z) = VI cos[(V2r)] at some approximate v3.98…

A: To use local linear approximation of the below function to approximate 3.98cos7.963π. fx=xcos2x3π

Q: Find the work done by F over the curve in the direction of increasing t. F = 3xyi + 4yj - 2yzk r(t)…

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Q: Determine the intersection point of the lines tangent to the curve r (t) = (senπt, 2senπt, cosπt) at…

A: The given curve is rt=sinπt,2sinπt,cosπt. Differentiating it with respect to t:…

Q: Evaluate F. dr where F = (x – 3y)i + (y – 2r)j and C is the closed curve in the xy plane, x = 2 cos…

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Q: 3. Find the work done by F over the curve in the direction of increasing t. = (2,x, y) = (sin t, cos…

A: Write the vector field F=zi+xj+yk The equation of the curve. rt=sinti+costj+tk Differentiate…

Q: Consider the function f: R R³ given by: t+1 f(t) = (; sin(cos(t)), tet t2 +4 Find f'(t) for all t e…

A: please see the next step for solution

Q: Consider the curve where a =0 (a) Compute(t) at t = [0, +∞). (b) Find the tangent line at the point…

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Q: Find the equation of the tangent plane to z = ey + x + x² + 7 at the point (5, 0, 38). = Z |

A: To find the equation of tangent plane to z=ey+x+x2+7  at the point 5,0,38In general the equation of…

Q: find the work done by F over the curve in the direction of increasing t. F = 2y i + 3x j + (x + y)k…

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Q: Use Green's Theorem to evaluate | F. dr, where F = (Va + 5y, 2x + Vỹ ) and C consists of the arc of…

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Q: Use Green's Theorem to evaluate / F · dĩ, where F = (VE + 3y, 2x + vũ) C consists of the arc of the…

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Q: Find the work done by F over the curve in the direction of increasing t. F=xyi + 8j + 6xk; C: r(t) =…

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Q: find the work done by F over the curve in the direction of increasing t F = 6z i + y2 j + 12x k r(t)…

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Q: (il) Find the point in which the tangent line to the curve F-12-30)1+ 2+Int'+ k at t=1 intersects…

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Q: Find an equation of the tangent line to the curve a = t sin t, y = t cos t att = 5. Lütfen birini…

A: Given,  x= t sin(t)y=t cos(t) To find : The equation of a tangent line. Solution: The slope of…

Q: The parametric form of the tangent line to the image of f(t)=⟨4t2,5t,t−2⟩ at t=3 is L(t)=

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Q: find the work done by F over the curve in the direction of increasing t. F = z i + x j + y k r(t) =…

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Q: Find the derivative 4cos4t sin4t O2cot4t O Other: -1/2 cot4t of the parametrically defined curve (t)…

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Q: The parametric form of the tangent line to the image of f(t) = (3t2,,t – 2) at t = 2 is L(t) =

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Q: Consider the parametric curve segment (t, t2), t ∈ [0, 1]. What is the firstorder derivative of the…

A: We have the given parametric curve t,t2, t∈0,1x=ty=t2 for t∈0,1the first order derivative the curve…

Q: Find the work done by F over the curve C in the direction of increasing t,where F=-5 yi+5xj+8z°k and…

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Q: F(x, y) = (e*, Find the integral of the function for the oriented curve that follows piecewise…

A: Given function is: Fx,y=ey-x,e2x