Find the terminal point P(x, y) on the unit circle determined by the given value of t. t = -5T P(x, y) = (

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

A:

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

A:

Q: = V4 cos" : – 1, y = 10 < x < 30

A:

Q: Q. Find the length of the arc of f(x) = ÷(x² + 1), 1< x < 4

A:

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: 1. Consider the curve C given by y = 5 + 2x3/2, 0 < x <1. (a) Find the length of the curve C.

A:

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

A:

Q: Find the arc length of the graph of the function y=2x32+3y=2x32+3 over the interval [0,9][0,9].

A: Here we have to find the arc length of the graph of the function y= 2x3/2 +3 over the interval [0,9]

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)

A:

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.

A:

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

A:

Q: y = 1/2 (e² + e^¹), − 1 ≤ x ≤1

A:

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

A:

Q: C) Find the arc length of the curve y-1-6x², 0≤x≤1

A:

Q: Find a path c(t) that traces the parabolic arc y = x2 from (0, 0) to (3, 9) for 0 ≤ t ≤ 1.

A: Given parabolic arc y=x2 from 0,0 to 3,9 for 0≤t≤1. The path ct that traces the parabolic arc has to…

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

A:

Q: Find an interval of t-values such that c(t) = (cost,sin t) tracesthe lower half of the unit circle.

A: Consider the given point as ct=cost,sint

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

A:

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

A:

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

A:

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

A:

Q: Find the length of the curve x=cos^2t, y=sin^2t, 0≤t≤Pi.

A: In this question,we find the arc length of the curve using x=cos^2(t),y=sin^2(t),0&lt;=t&lt;=pi Arc…

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

A:

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

A:

Q: 10. Circles tangent to the x-axis. Amm. [1+())- [yy +1+(.

A:

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

A:

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

A:

Q: For the curve x=3cos(t), y=4sin(t), find the value of d^2y/dx^2 at the point where t=π/5.

A:

Q: Find the exact length of the curve given by a = t° ,y (0 <t< 4). Length =

A:

Q: Find the length of the curve. 6t, , r(t) 0 <t< 1

A: Given:-r(t)=6t, t2, 19t3,         0≤t≤1since we have to find the length of curve.

Q: The Tschirnhausen cubic is the curve given by the equation x2 = y3 + 3y?. At which point(s) (x, y)…

A: Given query is to find the point of horizontal tangent.

Q: 10. Circles tangent to the x-axis. Amm. (1+() =[yy +1+(

A:

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

A:

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

A:

Q: Evaluate | yd x - x dy along the curve C shown in the figure. (a) (0,3) (3 ,0)

A:

Q: 10. Circles tangent to the X-axis. Amm. [1 + (y)*]° =[yy +1+(]".

A: Every function can be described through a differential equation. The differential equation defines…

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

A:

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: Q1. Find the length of the of the curve y = from x = 0 to x = 3.

A:

Q: n of the curve, L. (x+ 1)* , 0 0

A:

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 length of the curve r(t) = (e* cos t, et sin t , et), – In 4 <t<0.

A:

Q: Find the length L of the curve R(t) = 4ť²i + t° j+ 4k over the interval [3, 6]. L

A:

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

A: