2. Eliminate the parameter to find a description of the shape graphed by the para- metric curves given. Describe the shape and indicate the positive orientation. (b) x = 1-3 sin 4nt, y = 2+3 cos 47Tt, 0

Q: Suppose the curve C is given by the parametric equations x=1+ \t y=e' where t> 0. Find a equation of…

A: The equation of tangent line to the curve is given below

Q: Consider the following parametric curve. x = sin(8t) + cos(t), y = cos(8t) - sin(t) Find dy dx dy dx…

A:

Q: Find the exact slope of the tangent line to the 4 cos(t) parametric curve at the point ly = 7 sin(t)…

A: To Determine: Exact slope of the tangent line to the parametric curve :

Q: Which one of the following could be the graph of the curve given parametrically by x(t) sin(t + sin…

A: Given that x(t)=sin(t+sint) and y(t)=cos(t+cost).

Q: . Find an equation for the circle of curvature of the curver(t) = ti + (sin t)j at the point (pi/2,…

A: The parameterized curve are x = t , y = sin t The derivatives are                           y = sin…

Q: 3 The arc length of the portion of the curve y =x² with 0<x<4 is

A:

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

A:

Q: 13. Eliminate the parameter t, sketch the curve, and indicate the orientation. x=5 sint, y= 5cost,

A: We will square the both equations and then we will add them to eliminate the t

Q: Find an equation for the circle of curvature of the curve r(t) = 8ti +sin(5t)j  at the point (4pi,…

A: Consider the parametrized curve y = sin ((5/8)x). its derivative can be found as follows.

Q: 4. Sketch the graph of the curve y = Vĩ and the tangent line in the Cartesian Plane using a scale of…

A: Given curve y=x

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

A: SOLUTION-

Q: e Consider the CuLue defined by the eguation Y+ cos y = x+| for 0<y < 2TT. WIite an equation for…

A: Given that the equation is y+cosy=x+1,0&lt;y&lt;2π. It is required to write the equation of the…

Q: A curve is defined by the parametric equations: x(1) = e' cos t, y(t) = e' sint d²y dy and dr of the…

A: It is given that, x(t)=et cost,y(t)=et sint   It is known that, dydx can be found by chain rule and…

Q: A curve is defined by the parametric equations (t) = 8 cos(6t) and %3D y(t) 4 sin(-4t). Find . %3D

A: We have to find derivative

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: A curve is defined by the parametric equations sin z dz, CoS Z dz, t 2 1. y= X= Find the length of…

A:

Q: Which of the following is the equation of tangent line of the curve that is given by parametric…

A:

Q: Eliminate the parameter to express the curve in the form y = ƒ(x) . x = cos t, y = tan t

A: Given that, x=cost, y=tant We have to eliminate the t and express curve in the form y=f(x). As we…

Q: Find the arc length of the curve on the given interval. Parametric Equations     x = √t, y = 3t − 1…

A: Given: Parametric Equations x = √t, y = 3t − 1 Interval 0 ≤ t ≤ 1

Q: Consider the following parametric equation. x = 7(cos 0 + 0 sin 0) y = 7(sin 0 – 0 cos 0) 11 What is…

A:

Q: Use the arc-length formula of the parametric equation and evaluate the arc-length of the curve while…

A:

Q: 1. Find the moving trihedral and the curvature at any point of the curve R(t) = cos t î + sint ĵ+ k.

A:

Q: A curve is defined by the parametric equations cos z dz, sin z dz, t > 1. X= y= Find the length of…

A: Use the formula for the length of curve in parametric form.

Q: Find the arc length of the graph of the function over the indicated interval.

A:

Q: 10. Given the curve: y = 4cos°x – 3cosx, find the following values of x (from 0 to 2pi radians) when…

A:

Q: 1. Find the moving trihedral and the curvature at any point of the curve R(t) = cost î + sint j + k.…

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: 2 cos(t) T at the point 4 Find the slope of the tangent line to the parametric curve ly = 1 sin(t)

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Sketch the regions enclosed by the given curves. y = 2 cos(5x), y 2 sin(10x), x = 0, x = 1/10 2.0…

A:

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 cos(t) + In(tan(;t)), y= sin(t), n/4 <t < 3T/4. x = %3D Length = %3D

A:

Q: The unit circle x² + y = 1 can be wrriten in parametric form as x = cos(0) and y = sin0. dy Find and…

A: The unit circle can be written in parametric form as x=cosθ and y=sinθ We have to find dydx and the…

Q: 2. Determine the arc length of the given curves a) y =+ 1<y< 2 3

A: s=∫y1y2 1+x'2 dyy'=3y23-14y2y'=y2-14y2s=∫121+y2-14y22dys=∫121+y4+116y4-2×y×14y dys=∫12y4+116y4+12…

Q: Find an equation of the plane tangent to the following surface at the given point. 13 cos (xyz) =- 2…

A:

Q: Find an equation for the circle of curvature of the curve r(t) = t i + (sin t)j at the point (p/2,…

A:

Q: Find the length of the following curve using methods for parametric curves. x = 4 sin t y = 4 cos t…

A:

Q: A curve C has parametric equations X = tチ+1. dy (i) Find in terms oft. dx (ii) Show that there are…

A: We first find dy/dx

Q: Find the exact length of the curve. x = 9 cos(t) - cos(9t), y = 9 sin(t) - sin(9r), Ostsn 9 cos (47)…

A:

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

A:

Q: Eliminate the parameter to find a cartesian equation of the curve. x = sin(1/2θ),  y = cos(1/2θ),…

A: x=sin12θ,  y=cos12θ

Q: Consider the following. x = sin(6t),  y = −cos(6t),  z = 24t;    (0, 1, 4?) (a) Find the equation…

A:

Q: Find the exact length of the curve. x = 9 cos(t) − cos(9t), y = 9 sin(t) − sin(9t), 0 ≤ t ≤ pi

A:

Q: A cycloid has parametric equations z =t - sint, y = 1 - cost, 0 <t< 2x. Find the slope of the…

A:

Q: Find an equation of the tangent(s) to the curve with parametric equations E = t cos t, y =t sin t nt…

A: follow next step

Q: 23. Find (to two decimal places) the coordinates of the point P in Figure 9 where the tangent line…

A:

Q: Which of the following is the equation of tangent line of the curve that is given by parametric…

A:

Q: The unit circle x² + y=1 can be wrriten in parametric form as x = cos(0) and y = sin0. dy Find and…

A:

Q: 1. Find the tangent to the curve given by the parametric equations: X = 1/t; y= VE e-t

A: Appliaction of derivative problem

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.