Find the terminal point P(x, y) on the unit circle determined by the given value of t. t = - 7T 2 P(x, y) =

Q: m Find the equation of the tang ent to the curve ym =1 at the point (x1.y1). m

A: Topic:- application of derivatives

Q: Find the lengths of the following curves: b. x = cost and y = t + sin t, 0<t<n

A: we have to find the length of the given curve

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

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Q: Find the terminal point P(x, y) on the unit circle determined by the given value of t. t= - Zn 4…

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Q: Find the tangent to r(t) = (t +1, t², e') when t= 3.

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Q: Find T(t) and N(t) at the given point. X = = et cost, y = et sint, z=et; t = 0 T(0) = N(0) || =

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Q: Find the exact length of the curve (b) x = e' cos t, y= e' sint, 0<t<T

A: Length of the curve for parametric equation is given by:

Q: Find the length of the curve. x = cos t y = sin t

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

A: Given:    x = 2t    y = cos4t    0 ≤ t ≤ π/2

Q: Find the length of the given curve: where -4 < t ≤1. r(t) = (-2t, 2 sin t, 2 cos t)

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Q: Q6 Find the length of the arc of the curve in the given range, y3 1 16y + 4y2 + 3 x = 4(у + 4) + 4)…

A: Find Arc length

Q: 3t? Find the length of the curve x = t, y 2 osts 13. 3 =

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Q: Find the length of the given curve: r(t) = (-3t, -3 sint,-3 cos t) where-3 sts 5.

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Q: 64. Find the length of the curve y = 1 - e",0 SISI.

A: Formula to find the length of the curve helps to find the required length. Formula to find the…

Q: Find the lengths of the curves x = cos t, y = t + sin t, 0 … t … pi

A: Solution:Given   x= cos t,      y= t+sin t,   0≤t≤πFormula:Lenght=∫dxdx2+dydt2dt1+cos 2x=2 cos2…

Q: (e) Find the exact length of the curve. x = e cost, y = et sint, 0 ≤ t ≤n.

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Q: The line y = mx + 1 is a tangent to the curve y2 = 4x .Find the value of m

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Q: y = 1/2 (e² + e^¹), − 1 ≤ x ≤1

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Q: a)Find the exact length L of the curve 3y? = (4x – 3)°, 1 0. Answer: b) Evaluate Sxe*dx Answer: 1 c)…

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Q: Find the point (x,y) of x^2+14xy+49y^2 = 100 that is closest to the origin and lies in the first…

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Q: Find the point (x, y) of x² + 14xy+49y = 100 that is closest to the origin and lies in the first…

A: we draw a shortest straight line from origin to line, which will we perpendicular then we will find…

Q: I= e", y =t e", teR,

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Q: Find the length of the curve. V2 ti + e'j + e-tk, 0 <t< 8

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Q: Find the length of the curve. r(t) = (4t, 0 <ts 1

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

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Q: a)Find the exact length L of the curve 3y = (4x – 3), 1 0. Answer: b) Evaluate xe*dx Answer: .3 c)…

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Q: A particle P moves on the curve r= 3i + 4t²j. The distance of P from the origin when t =1 is

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Q: Find the exact length of the curve. 43. x = t sin t , y = t cos t , 0 ≤ t ≤ 1

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Q: Find the length of the curve r(t) = (1,t2, t³). 0<t < 1.

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Q: Q5 Find the length of the arc of the curve in the given range, y3 3 ' 4(y + 5) 1 x = 25y + 5y2 +…

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Q: Find the radius of the osculating circle for 7(t) = (cost+t sin t)i +(sint – t cost)j +3k when t=1.

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Q: At the given point, find the line that is normal to the curve at the given point. 6x <y - TT Cos y =…

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Q: Find all points on the curve where the tangent line has the given slope. (If an answer does not…

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Q: Find the points on the curve C where the tangent is horizontal C: x = t + 6t, y = t' – 3t. O A.…

A: First we have to calculate dy/dt then,we have to find out the value of t for which dy/dt =0 To find…

Q: Find the lengths of the curves x = cos t, y = t + sin t, 0≤ t ≤ π

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Q: of the curve yln x + 5x² + y' =13 at the point (1,2) dx b) Find

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Q: Find the length of the curve 7(t) = (ei cos(), ei sin(÷), e) n(4),e¿): for 0 <t < 5. CoS

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Q: (d) Calculate the length of the arc of the curve y=; (+1)* between the ordinates t = 0.5 andt = 2.5.

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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 exact length of the curve (a) x = 1+ 3t2, y = 4+ 2t³, 0<t<1 (b) x = e' cost, y = e' sin t,…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: The point on the curve x? + 2y = 0 that is nearest to the point (0,-;) occurs where y'is A) 0 B)…

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Q: Determines the length of the curve in the indicated interval x = 3 sin t+ 3t, y = 3cos t, 0stsm O 12…

A: Given curve is x=3sint+3t and y=3cost, 0≤t≤π. We have to determine the length of the curve on the…

Q: Use the formula below to find the length of the curve defined by the equation x= cos^2 t , y = sin^2…

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Q: Find the length of the curve. r (t) = v2ti + e'j+e-*k, 0 < t < 5 L =

A: first we calculate the derivative for each component of given vector we get,        r'(t) = √2 i +…

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

A: we have to find th length of the arc for the given curve .

Q: Find the equation of the tangent to x = = VE , y = t – at the point where t = 4. Note: Sample format…

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Q: Q6 Find the length of the arc of the curve in the given range, y3 x = 16y + 4y² + 0<y< 4 %3D 3 4(y +…

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Q: Q5 Find the length of the arc of the curve in the given range, y3 + 3 1 x = 25y + 5y2 + 0sys 3 4(y +…

A: "Since you have asked multiple questions, we will solve first question for you. If you want any…

Q: Find the exact length of the curve (x=t?cost ly=t?sint Osts2n (n? + 4)3/2 - 4] 3 a. 4 + 4)3/2 – 1]…

A: The given implicit function is,  x=t2cost, y=t2sint0≤t≤2π