*star_border*

## Related Calculus Q&A

Find answers to questions asked by students like you.

Q: Let C be the curve defined by 7(t) = (2+2 sin(t), 3 – 2 cos(t)) for 0 <t< L (e + 4z) dz + (2zye" +…

A: Click to see the answer

Q: Let F = ( ) 5x* + 16z, 2x³ + 3y² + 16z, x + y + eVz³+1 and C be the curve defined by 7(t) = (2…

A: Given that, F=5x4+16z, 2x3+3y2+16z, x+y+ez3+1 And rt=2cost, 2sint, 16cos2t sin2t, o≤t≤π To find…

Q: Let C be the curve.

A: Click to see the answer

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

A: Click to see the answer

Q: What are the critical points for the plane curve defined by the equations æ(t) = sint + cos(t), y(t)…

A: Critical points.

Q: find y'' for the curve cosx-siny=4

A: Click to see the answer

Q: Let C be the curve defined by r(t) [6 cos(t) – 5 cos (t), 6 sin(t) – 5 cos(t) sin(t), cos(t)] for 0…

A: Click to see the answer

Q: 3 Consider cune detined by y cos (T2) =UY +y+2 2 ) Verify point (2,-2) belongs to this curve, fond…

A: Click to see the answer

*question_answer*

Q: Consider the curve x = et-5 cos t, y = et-5 sin t, 0 <t < 2n. a) Find the values of t where the line…

A: The slope of a tangent to the curve y=f(x) at x=a is f'(a). If the tangent is vertical to the curve,…

*question_answer*

Q: Consider the curve x = et-5 cos t, y = et-5 sin t, 0 <t < 2n. a) Find the values of t where the line…

A: Click to see the answer

*question_answer*

Q: 4. Find an equation for the tangent plane to the surface z = 3x + 5y + arctan in the point (0, 1,…

A: Click to see the answer

*question_answer*

Q: - Sva cos 2t dt from x= 0 to x= Find the length of the curve y =

A: Click to see the answer

*question_answer*

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−lnx if 18≤y≤e28−1 ⇒f(x)=18x2−lnx if 1≤x≤e The arc length of the portion of the graph…

*question_answer*

Q: Let C be the curve defined by T(t) = (2 + 2 sin(t), 3 – 2 cos(t)) for 0 < t < 4x=²) dx + (2xyev" +…

A: Given the integral is ∫Cy2exy2+4x-2dx+2xyexy2+2dy. Rewrite the integral as ∫CF·→dr→:…

*question_answer*

Q: Consider a curve parameterized by: c(t)=(sin^3(t),cos(t)) Compute dy/dx at the point ((sqrt(2)/4),…

A: Differentiate the given function as follows.

*question_answer*

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

A: Click to see the answer

*question_answer*

Q: i) Find the length L of the curve y = x + cos x, 0<x <T/2 Use any one of the following formulas 2…

A: Click to see the answer

*question_answer*

Q: 3. Find the length of the curve y = In (cos x), 0 <x <

A: we have to find length of the curve

*question_answer*

Q: The parametric equations of a curve are given by x = In (VE +1) and y = cosh-' (2t). dy when t = 1.…

A: Given x=lnt+1 and y=cosh−12t We have to find the dydx when t=1 We know that dydx=dydtdxdt.....1…

*question_answer*

Q: The parametric equations of a curve are given by x = In (VE +1) and y = cosh-(2t). dy when t = 1. dx…

A: Click to see the answer

*question_answer*

Q: Consider a new curve Č parametrized by r(t) = (cos t esint, sin t- cos t), 0 <t <I but with F still…

A: Click to see the answer

*question_answer*

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…

*question_answer*

Q: Compute Sc(2x + V) ds, where C is the curve from (0,0) to (2, 4) along y

A: Given

*question_answer*

Q: Let C be the curve parameterized by r(t) = (cos(t), sin(t), /3t), 0 <t < 1/2. Calculate 1. |r'(t)| =…

A: Given:- r(t)=<cos(t),sin(t),√3t > To find:-

*question_answer*

Q: Find orthogonal trajectory to the curve given by r = a(1 + cos θ)

A: Click to see the answer

*question_answer*

Q: A particle moves in the xy-plane in such a way that its path is defined by x = et cos t and y = et…

A: Given that, x=etcost, y=etsin2t. Differentiate x with respect to t, dxdt=etcost-etsint=etcost-sint…

*question_answer*

Q: Find the lengthof the curve r = a sin² (0/2), 0 0

A: Click to see the answer

*question_answer*

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

A: We will solve the following

*question_answer*

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 :…

*question_answer*

Q: Compute ∫C(2x+√y)ds, where Cis the curve from (0,0) to (2,4) along y=x^2.

A: Click to see the answer

*question_answer*

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

A: Given: y=18x2−lnx18≤y≤e28−1

*question_answer*

Q: Find the length of the curve. r(t) = cos(2t) i + sin(2t) j + 2 In(cos(t)) k, osts n/4

A: Given:

*question_answer*

Q: Obtain the gradient to a curve with the parametric equations given by I = In - and y = sinh 2t whent…

A: Click to see the answer

*question_answer*

Q: Find the arclength of the curve x = 3 cos(5t), y = 3 sin(5t) with 0 <t< 20 %3D

A: Click to see the answer

*question_answer*

Q: 8. Find the length of the curve defined by x = cos(2t), y = sin(2t) from t = 0 to t = n.

A: If x = f(t), y = g(t) in (a, b) then length of the curve is,

*question_answer*

Q: Find the arclength of the curve x 5 cos(3t), y = 5 sin(3t) with 0 <t< 6

A: Click to see the answer

*question_answer*

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.

A: Click to see the answer

*question_answer*

Q: Show that 22 dz = 0 1 – cos(2) whenever y is a closed simple smooth curve contained in a very small…

A: Solution: Here the integral is ∮+γz21-cosz We know that cos0=1cos2π=1cos3π=1... Only z=0 is in…

*question_answer*

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

A: Click to see the answer

*question_answer*

Q: Find the unit tangent vector to the curve defined by F(t) = (4 cos(t), 4 sin(t), 3 sin (t)) at t = 3…

A: Click to see the answer

*question_answer*

Q: Find the arclength of the curve: y = 5(x +2)3/2, 2<x<7

A: Given: Find the arclength of the curve : y=5(x+2)^3/2 ,2<=x<=7

*question_answer*

Q: Find the arclength of the curve: y = 5(x + 2)3/2,2 <x<7

A: The arc length is given by, S=∫ab1+f'x2dx Find the derivative of the function y=5x+23/2.…

*question_answer*

Q: Find the derivative dydx of the hyperbolic spiral r=aθ.

A: Click to see the answer

*question_answer*

Q: Suppose a curve is defined by: x/x-y=y2-1 FIND dy/dx

A: Given curve is xx-y=y2-1 Divide rule of differentiation state as: ddxuv=vddxu-uddxvv2…

*question_answer*

Q: Suppose that a particle following the path (e' cos(t). sin(), ) flies off on a tangent at lo = 2.…

A: Click to see the answer

*question_answer*

Q: Find the length of the curve. r(t) = cos(6t) i + sin(6t)j + 6In(cos(t)) k, 0 <t< n/4

A: Click to see the answer

*question_answer*

Q: Find the orthogonal trajectories of the family of curves r 5C sin 0, where C being parameter.

A: Follow the below steps to find the orthogonal trajectories. Differentiate the function with respect…

*question_answer*

Q: Find an equation of the plane tangent to the following surface at the given point. 1 sin (xyz) =

A: Click to see the answer

*question_answer*

Q: 7- Find the leng thof the Curve arce 34 from to y=4

A: Click to see the answer