Find the exact length af te of the curve, 2. x-

Q: 3. What is the length of the curve r = cos3 (-) where 0 < 0 <: sos

A: See the attachment

Q: 5. Trace the curve r = sinocos³o.

A: Given curve: r=12sinθ cos3θ

Q: (a) Compute the arc (1,3, 1/3). F(t) = (t, 3, t) between the points (0,3, 0) and length of the curve

A: These 2 are unrelated problems as anyone can be solve without any help of another. So by Bartleby…

Q: = V4 cos" : – 1, y = 10 < x < 30

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Q: Find the exact length of the curve.

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Q: 3. What is the length of the curve r = cos3 (-) where 0 < 0 <- 4

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Q: Find the length of the curve over the given interval. r = 1 + sin θ, [0, 2π]

A:

Q: :If the tangent at (a, b) to the curve x³ + y° = c° meet the curve again in (a,,b,). b, Prove that…

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Q: Which of the following expressions gives the length of the curve defined by R(t) = tij +In tk…

A: We have to find arc length expression for the given vector function. Given is the curve…

Q: If C = {(x, y): 1 ≤ x ≤ 2, y = ln(x + √x² − 1)}, find the length of the curve. -

A: C=x,y: 1≤x≤2, y=lnx+x2-1

Q: find the length Of the Curve fram this merval to

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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: Find the length of the arc of y=x^(3/2) between the points (1,1) and (4,8).

A: Find the length of the arc of y=x^(3/2) between the points (1,1) and (4,8)

Q: (B) The length of the curve r(t)=(1+1i+(1-nj+rV2k from the point t= to the point t=; is 2. - 112

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Q: The arc length of the curve y=3-4x2, where 0<x<1is [1-37/37] O 54 /37-1] 54 1-/37] O, 54 4 137/37-1]

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Q: Find the exact length of the curve. 23/2, Osxs 6

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Q: Find the length of the curve. r(t) (7t, 3 cos t, 3 sin t), -2 sts 2

A:

Q: 3. For the curve y = 3xtnx at the point (1,1) find the following using exact numbers:

A: Given y=3xlnx at point 1,1

Q: Find the length of arc of the curve 6xy = x^4 + 3, from the point where x=1 to the point where x=2

A: The given curve is: 6xy=x4+3 y=x46x+36xy=x36+12x Differentiate it: dydx=3x26-12x2dydx=x22-12x2

Q: Find the length of the arc of the curve in the given range, x3 + 3' 4(x + 5) ' 1 y = 25x + 5x²+…

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Q: If lx + my = 1 touches the curve (ax)" + (by)" = 1, show that %3D )+) = 1.

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Q: Given the OC + xY +2y2 3D6 curve Find the Coordinates of all other Poīnts on the Curve with slope…

A: x+xy+2y2=6 Slope of the curve is the derivative of the given curve at the given point. So…

Q: Find the arc length of the segment of the curve between the lines x-1 and x-16

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

A:

Q: y= In x

A: Given function is y=x/ln(x)

Q: Find the 0lar eauatiDo for the curve represented by the given Cartesian euation.

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Q: Use the arc length formula to find the length of the curve y = 2-3x, -2 is less than or equal to x…

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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 the exact length of the curve. x = et − t,    y = 4et/2,    0 ≤ t ≤ 2

A:

Q: 12) Find the exact length of the curve [4,16] on 3

A: We can find the exact length of the curve as below,

Q: Find the exact length of the curve. x = e' +", Osys 4

A: Given function is  x = e^y +(1/4)e^-y

Q: Find the exact length of the curve. y = In(1 - x²), o s x s

A: Solve the problem using definite integral

Q: Find the length of the curve. Vzti + etj + e-tk, Osts 3

A:

Q: Find the arclength of y = 3x2 -5 on x is greater than or equal to 0 and less than or equal to 2

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Q: Find the length of the arc of the curve x2 = (y − 2)3 from P(1, 3) to Q(8, 6).

A:

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 exact length of the curve. y = 2 In(cos (÷)) Tt/3 < x <T/2

A: Here given Differentiate the given function with respect to x using the chain rule of derivative

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

A:

Q: Find the exact length of the cur curve. y = Vx- x2 + - sin (V)

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Q: 1. y = 1 - x; A(1,0), B(8,-3)

A: According to the company rule, we can answer only the first question and rest can be reposted

Q: the Q2, Find hergth of o polor Curve ア= B4 Use this formula dr de

A: Given:  The polar curve is given byr=eθ2 To Find:  To find the length of the given polar curve by…

Q: Find the arc leng th of the curve given by Ost s2

A:

Q: Find the length of the curve. r(t) = (3t, 3 cos(t), 3 sin(t)), -3 sts 3

A: For the curve r(t) = f(t) , g(t), h(t)On the interval [a, b]The length is given by L =…

Q: Consider the curve y = – In|cos(x)| as x travels from T to 6 a) Find the length of the curve.

A: Hi, since you have asked multiple questions, we will solve the first question for you. If want any…

Q: Fined the arc leng th of the curve

A:

Q: Find the arclength of the curve x = - with 3 ≤ t ≤ 4.

A: Given x=13t3, y=12t2 with 3≤t≤4

Q: y = In(1 – a²) ; 0 < æs

A: Solution:-

Q: Find the exact length of the curve. y = In(1 - x²), o sxs

A: Find dy/dx, then put it in the arc length formula.

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.