Find all of the points where the curve r = 2 cos (θ/3) intersects thecircle of radius √2 centered at the origin.

Q: Find fe F dr for F = 7yi - (sin y)j on the curve counterclockwise around the unit circle C starting…

A:

Q: Find the length of the curve 7(t) = (4 cos(3t), 4 sin(3t), 4t) for – 4 <t < 2 Give your answer to…

A:

Q: = V4 cos" : – 1, y = 10 < x < 30

A:

Q: Find the arc length of the curve from z = 3 to = 6. Leave your answer as a simplified radical. f(x)…

A: Explanation of the answer is as follows

Q: Set up an intergal of the Curve for the length 3T Y%3DZE* sin (x), O4 xE 2

A:

Q: Find the length of the curve 7 (t) = (3 cos(t), 3 sin(t), 5t) for – 4 <t <1 Give your answer to two…

A:

Q: Find an equation of the tangent to the curve given by = evi y = t – In(?) at the point corresponding…

A:

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

A:

Q: Find f F. dr for F = 2yi – (sin y)j on the curve counterclockwise around the unit circle C starting…

A:

Q: Find the length of the curve over the given interval. r = 4 sin θ, [0, π]

A:

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

A:

Q: Find the length of arc of the given curve. 5. R= (sin 2t , cos 2t , 2t³/2), 0 sts1.

A:

Q: The curves r¡(t) = (2t, t², t³) and r2(t) = (sin(t), sin(3t), 2t) intersect at the origin. Find…

A: If there are two curves y=f1(x) and y=f2(x) which intersect each other at point (x0, y0).  The angle…

Q: Find an interval of t-values such that c(t) = (cos t, sin t) traces the upper half of the unit…

A: Interval.

Q: Find an equation for the tangent plane to z = cos(x2 + y2) at the point /等,0).

A:

Q: Show that the exact length of the curve below is y = Vr - r² – sin ¬1 (V7)

A: SOLUTION-

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

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

Q: Find the length of the arc of x²+y²=64 from x=-1 to x=-3, in the second quadrant.

A: Given curve: x2+y2=64

Q: Find the arc length of the graph of the function over the indicated interval. x2 3/2 + 1 y = y 4 1 3…

A:

Q: Find the length of the curve 7 (t) = (3 cos(4t), 3 sin(4t), 4t) for –5 <t< 8 Give your answer to two…

A:

Q: Sketch the following curves 2. y = sin(x) + v3 cos(x) on [–27, 27].

A:

Q: Find the exact length of the curve. x = 7 cos(t) – cos(7t), y = 7 sin(t) – sin(7t),

A: given : formula for arc length is as below :

Q: Find the speed of the cycloid c(t) = (2t – 2 sin t, 2 – 2 cos t) at points where the tangent line is…

A:

Q: Find the speed of the cycloid c(t) = (4t −4 sin t, 4−4 cos t) at points where the tangent line is…

A:

Q: The curves r₁(t) = (5t, t², t3) and r₂(t) = (sin(t), sin(5t), 4t) intersect at the origin. Find…

A: see my solution below

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: Find the length of the curve 7(t) = (cos(4t), sin(4t), 5t) for – 8 <t< 1 Give your answer to two…

A: use the arc length formula for finding length.

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 x=1+2sin at, y=3–2 cos at, 0<t<l

A:

Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

A: The given question is the application of integration and solved as shown in step2.

Q: Find the point on the cycloid c(t) = (t − sin t, 1 − cos t) where the tangent line has slope 1/2.

A:

Q: Find the length of the curve y = ln (cos x), 0&lt;= x&lt;= pai/3

A:

Q: Find the exact length of the curve. y = In(sec(x)), 0<x< 1/3 In (2 + v 2 ) – - In (1)

A: Since you have posted 2 questions we will solve one for you please resubmit the question. Given:…

Q: ind all the tangents to the curve y cos (x %3D

A: Here we have to find the tangents on the curve y=cos(x+y)...........(1)     , -2π≤x≤2π parallel to…

Q: Find the arc length of the graph of the function over the interval. y = In(sin z);

A: Given,          y=lnsinx ; π4,3π4

Q: Find the length of arc of the given curve. 5. R= (sin 2t, cos 2t , 2t³/2), 0 sts1.

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 = 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 lengthof the curve r= a sin² (0/2), 0 s0s T, a>0

A:

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

A:

Q: Find the length of the curve 7 (t) = (4 cos(5t), 4 sin(5t), 5t) for – 3 < t < 9 Give your answer to…

A: Given: r→t =4cos(5t), 4sin(5t), 5t  for -3≤t≤9

Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

A: To use the geometry we will change the polar equation into the cartesian equation first.  For that,…

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

A:

Q: The parametric form of the tangent line to the image of f(f) = (4i², 2,t – 3) at t = 2 is L(t) =

A: To find the parametric form of the tangent line to the image of f(t)

Q: Find an interval of t-values with t > 0 such that c(t) = (cos t, sin t) traces the upper half of the…

A: Given,  ct = cost, sint  and t ≥ 0 We have to find the interval of t-values such that ct = cost,…

Q: Find the lengthof the curve r= a sin (0/2), 0s 0S T, a>0

A: The formula for finding arc length is L = ∫0πr2+ drdθ2dθ, where r = a sin2(θ2)

Q: Find the length of the curve r(t) = (cos(3t), sin(3t), 4t) for -6 ≤ t ≤ 5 Give your answer to two…

A:

Q: Find F. dř for F = 5yi – (sin y)j on the curve counterclockwise around the unit circle C starting at…

A:

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.