1. The parametric equations for the astroid below are x = sin' (t), y =- cos (1) on 0

Q: The equation of the tangent line to the parametric equations, x = sine, y= 20 + cose at 0 = 0 is y =…

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Q: The parametric equations for the paths of two objects are given. At what rateis the distance between…

A: Given: The parametric equations for the paths of two objects are given. At what rateis the distance…

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

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Q: 18. Find the second derivative of y with respect to x of the following parametric equations. x = 1 +…

A: Using derivatives of parametric equations.

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: Find the derivative dydx of the polar function r=1+sinθ at θ=π4.

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Q: Consider the curve defined parametrically by x(t) = cos(t), y(t) = sin(t), te [0, π] (a) For what…

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Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

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Q: #3. Find parametric equations for the tangent line to thể curve with parametric equations x = (sin…

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Q: Find parametric equations for the tangent line to the curve with the parametric equations x…

A: Given: The parametric equations, x = t2+3,  y = ln t2+3, z = t and the point 2, ln4, 1. To find: The…

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

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Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: Given:

Q: 1 For the following parametric equation x(t) = tan t and y(t) = sec t find the tangent line passing…

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Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

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Q: A curve is defined by the parametric equations Find the length of the curve from t=1 to the closest…

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Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

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Q: (1) Consider the ellipse a2-xy +y? = 1. Using implicit differentiation find . Find all values of x…

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Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: Given To find parametric equations for the tangent line to the curve with the given parametric…

Q: 1. x (0) = 0 + cos 0 y (0) = 1+ sin 0 given that

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Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: The tangent line to a parametric curve given by c(t)=< x(t) , y(t) , z(t) > at some point…

Q: Find the equation of the tangent line to the parametric curve at the indicated point. Show all work.…

A: Equation of tangent line : y - y0 = m ( x - x0 ) m is the slope of tangent line .

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: The given parametric equation is: x=5 ln t  ,   y=4t   ,      z=t3 Given point is:  (0, 4, 1) From…

Q: Eliminate the parameter t from the parametric equationsx =3 +sin t and y = cos t - 2.

A: Given: x=3+sint and y=cost-2 We have to eliminate the parameter t from the parametric equations.…

Q: Find the total distance traveled by a particle along the curve given in parametric form x=sint -t…

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Q: 9. Show that the curve with parametric equations x = sin t and y = sin(t + sin t) for 0st s 2n has…

A: Given that the curve with parametric equations are x=sint,y=sint+sint. First find the slope that is…

Q: Show that the curve x = 3 cos(t), y = 2 sin(t) cos(t) has two tangents at (0, 0) and find their…

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Q: Find parametric equations for the tangent line at the point (cos(), sin(5 ), ) on the curve a = cos…

A: Here, the given parametric equation of the curver(t)=(x,y,z) where x=cos t, y=sin t, z=t. To find…

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: Here we have to find the parametric equations for the tangent line to the curve with the given…

Q: Suppose a curve is defined by the parametric equations x=sin(t) and y=cos(t) i) Find the points…

A: Explanation of the answer is as follows

Q: Find an equation of the tangent(s) to the curve with parametric equations x = 1+ vt, y = e at the…

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Q: . Find the parametric equations for the tangent line to the Curve at the Specific point. X = e-t cos…

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Q: x = 2 cos(3t) – 4 sin( 3t) IT t = 2 y = 3 tan( 6t)

A: given,        x=2cos3t-4sin3t   and y =3tan6t

Q: Find the points (z, y) at which the polar curve r = 1+ sin(0), – sos has a vertical and horizontal…

A: The polar curve is r=1+sinθ. Suppose that x=rcosθ and y=rsinθ. That is,…

Q: Find the points (x, y) at which the polar curve r = 1 + sin(0), – < 0 has a vertical and horizontal…

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Q: A curve has parametric equations x = 2 sin t ,y = cos (2t) + 2 sin t for −π/2≤ t ≤−π/2 . Find out…

A: Given : parametric equations x = 2 sin t , y = cos (2t) + 2 sin t for −π/2 ≤ t ≤ π/2     Note :…

Q: Find the slope of the line tangent to the following polar curve at the given point. 3x r= 3-3 sin 0;…

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Q: x = 2 cos(t) Find the slope of the tangent line to the parametric curve at the point y = 3 sin(t)…

A: The derivative dydx defines the slope of the tangent drawn to the curve.

Q: 3. x = 3+ 4 sin t ;y == 3 cos t – 4

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Q: The length of the curve determined by equations x = 8 cos t + 8t sin t and y = 8 sin t – 8t cos t…

A: Given: x=8cost+8tsinty=8sint-8tcost0≤t≤π2

Q: Determine the (1) graph, (2) initial and terminal points, (3) orientation, (4) the dy derivative and…

A: x(t)=3+sin(t), y(t)=-2+cos(t)   where π≤t≤2π   Graph

Q: 8/3 Find the slope of the tangent line to polar curve r = 8 sin 0 at the point 3.

A: Explanation of the answer is as follows

Q: Find the second derivative of y with respect to x from the parametric equations given. x = 3 + 4…

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Q: Determine the (1) graph, (2) initial and terminal points, (3) orientation, (4) the dy derivative ,…

A: Formula: sin2 t+ cos2 t=1 The given parametric equation is: x(t)=3+ sin(t) and y(t)=-2+ cos(t) where…

Q: r(t) = (e-t cos t, e-t sin t, e-t)

A: Given  rt=e-tcost,e-tsint,e-t First find derivative of given point dxdt=-e-tcost-e-tsint…

Q: x = 3 ln(t), y = 4t1/2, z = t3; (0, 4, 1)

A: Given Data: x=3lnt ......1y=4t1/2  ......2z=t3      ......3 x0, y0, z0=0, 4, 1   For the specified…

Q: Show that the curve x = 3 cos(t), y = 2 sin(t) cos(t) has two tangents at (0, 0) and find their…

A: on solving this we get

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: We find parametric equations for the tangent line to the curve with the given parametric equations…

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

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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.