Find the length of the spiral r=θ for 0≤θ≤4

Q: Find the length of the curve given by c(t) = (t*, t², tº), for t E [0, 1].

A: Given:- C(t) =(t4 , t2, t0 )  To find:- Length of curve [0, 1]

Q: I Find the acute angle between the two curves xy = 3 and x2 = 9y

A: Given data: First curve xy=3. Second curve x2=9y.

Q: Find the length of the arc of the curve in the given range, y3 1 x = 16y + 4y? ++ 0sys4 4(y + 4) '

A:

Q: The length of the curve y= is equal to x =3: from to 을(x2 + 2) O a. 12 Ob. 1 O c.9 Od. 3

A: We can use the application of integration in order to solve the given problem.

Q: For numbers 11-14 consider trapezoid LOAF. L E F

A:

Q: The equation of the tangent line to the curke x? + y = 36, at (6,-16) is %3D y = (x+6) + 16 16 16 16…

A: we have to find the equation of the tangent line to the given curve at (6, -16)

Q: Find the exact length of the curve. y= In{1 – x²), o s 1. 0 sxs! 7. I Ju =

A: We will find the exact length of the curve as shown below

Q: Given * = (1+ a -- 14) dy 2 5 3 2 What is the value of k such that y is parallel to the curve

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Q: Find the length of the curve y = x³/2 from x = 0 to x = 5. O 12.407 O None of these O 14.702 O…

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Q: Find the length of the curve given by ř () = (6t, 12/T, 3Int) for 1<tse. O 8e-4 O 2e-1 O 4e - 2 O…

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Q: Find the distance between the skew lines defined by L1: ri(t) = L2:r5 (s) =

A:

Q: The Composite Trapezoidal Rule applied to the itegral I = gives the error E = 12 Suppose 2+2r -e…

A: The double derivative test is used to optimize (maximize or minimize) a function. Follow the steps…

Q: Find 2"dz for the case of z(= a) # z(= b), and when the curve is closed, that is when a b.

A: Note: We are not given any specification of n and the curve C. So, we have taken various cases here.…

Q: What is the length of the latus rectum for the curve, (x + 3)2 + 4(y – 1)² = 4 а. 2 O b. 1 О с. 4 O…

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Q: Find the length of the curve. y = 2 – 4x, 1<a< 3 O 54 3V17 O 17 O 2y17

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Q: use Lagrarge mul tipliers Sublect to the Constcair t to mekim,ze x+2y=5

A: Consider the given information. fx,y=x+4xy+6y and x+2y=5 Now, make the auxiliary function.…

Q: Find the length of the spiral r = eθ/√2 from θ = 0 to θ = π.

A: Given Differentiating r with respect to thita ,we get

Q: The length of the curve y = from x = 0 to x 6 is

A:

Q: compute the length of the curve over the given interval. r(t) = 2ti − 3tk, 11 ≤ t ≤ 15

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Q: w Find the lengths for the fallowing curvers tar=lt cose 2.

A: find the length of both polar curve as following:-

Q: 4. Find the length of the arc C = {(x, y): y = V16 – x²?,0 < x < 3}.

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Q: y = e*, 0<z<1.

A:

Q: Find orthogoral trajectory to the family of dircles 3 x² + y? = 2Cy.

A: We have given equation of curve x2+y2=2Cy Then, differentiate both sides we get…

Q: Find the length of the curve given by S(x) = (a -) defined on the interval (1, 2].

A: Consider the given curve:

Q: Find T N ¢B for the carve at the indlicated pont Carレe posnt r(t) = at

A: Given

Q: Find the length of the curve given by c(t) = (t*,t²,tº), for t E [0, 1].

A:

Q: Find the length of the curve. x=(y - 1) 3/2 from y = 1 to y = 4 O 7 O 10 21 2 O 1

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Q: Find the length of the curve y = V- from z =1 to r = e. 3

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Q: Find the length of the curve r= e2θ, 0≤θ≤2

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Q: Find the exact length of the curve. X = Vу (у — 3), 16 <y S 25

A: First differentiate wrt y

Q: Use this formula to find the curvature. y = 3x4 K(x) =

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Q: Find the length of the curve y=z from z 0 to z=4.

A: The length of the curve is given by:

Q: Find the length of the arc of the curve in the given range, y3 3 4(y + 5) ' 1 x = 25y + 5y? + Osys3

A:

Q: Given ZY = 25, What is the distance from ZS %3D U W T. S Y

A: Given:

Q: O Find the length of the following curves 4/2 3/2 + Dx, 0<I<1, 3 i) y(r) = 21 ii) 1 = ² + 21, y=…

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Q: Find the length of the curve given by r(t) = for -5 <t<5. O 5/19 O 10/10 O 10/19 O 5/10 O 10

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Q: Find the exact length of the curve. x = et + e=t, y = 5 – 2t, 0st< 4

A: The solution are next step

Q: For what values of a and b is the line-5x +y b tangent to the curve y = ax when x = 37 a = b D %3D…

A: Given: Equation of line is -5x+y=b. Equation of curve is y = ax3 .

Q: Find the length of the curve over the given interval. r = 2a cos θ, [−π /4, π/4]

A: Since, we have to find the length of the curve over the given intervalr=2a cosθ over the interval…

Q: Find the length of the following curve (a) x = 2t , y = cos 4t, 0 <t<

A:

Q: Find the length of the arc of the curve in the given range, y3 +. 3 1 x = 16y + 4y² + 0 < y< 4…

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Q: Find the length of the curve. 2ti + etj + e k, 0<tS 4

A:

Q: Find the length of the arc of the curve in the given range, x = 16y + 4y2 + ン3 +. 3 4(y + 4) 0 < y<…

A: In the question we have to find length of Arc of the curve.

Q: Find the length of the curve 7 (t) (9 In(t), 4t?, 12t) for 1 <t < 6

A: The given curve is r→t=9lnt, 4t2, 12t for 1≤t≤6 We have to find the length of this curve.

Q: Find the length of the arc: C: x= 3t2 +2, y = 2t3 –1, 1st<3.

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Q: Find the length of the indicated portion of the trajectory. r(t) = (1+2t)i + (1+8t)j + (4 – 4t)k, –…

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Q: B- Use the Trapezoidal rule with n=2 to estimate dx, to find the absolute relative true error |E,?

A:

Q: The length of the curve y from x=0 to x= 6 is

A: We need to find the length of the curve  y=23(x2+1)32 from x=0 to x=6

Q: Find the exact length of the curve. y = In(sec x), 0s x s a/3

A: This question is based on application of Derivative.

Q: Find the length of the curve. r(t) 4 it2j3k, 0 st s 1

A: Consider the curve x = 4, y = t2 and z = t3.The derivatives are