A curve Cis given by the parametric equations z = 2t –2 and y = (t- 2) where t > 0. 1. The curve has a vertical tangent line at the point O(0, 4) O(0,0) O(0,-2) O(1,-1) O(1,0) O(0, -1) 2. Is the point (-8, 8) lies on the curve C? OYes ONO

Q: 5. The curve C has parametric equations = (In t)? – Int, y = In t2 - t2, (1) Find the exact…

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Q: Suppose parametric equations for the line segment between (1,9) and (0, Sx(t) = a + bt ly(t) = c+ dt…

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Q: find the parametric equations for the tangent line to the curve x=t^2-1,y=t^3+1,z=t^2 at the point…

A: Given, x=t^2-1 y=t^3+1 z=t^2 point (x1,y1,z1)= (8,28,9)

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

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Q: Find the equation for the line tangent to the parametric curve: x = t^3 - 9t y = 9t^2 - t^4   at…

A: Find slope and then use equation of tangent line

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

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Q: Eliminate the parameter f in the parametric equations z(t)=√t+1, y(t) = Sketch the graph of the…

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Q: 2. Let F(x, y, z) = (6xyz+4x) i+(3x² z+ze=v)j+(3x²y-e-") k, and let C be the portion of the…

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Q: 3. Consider the parametric curve C given by * = te', y =t + cos t. (a) Find the equation of the…

A: Given: The parametric equation of the curve C is  x=tet, y=t+cost (a) To find: The equation of…

Q: the length of a parametric curve: x = 2t + 1 ; y = t2 - 3 ;  0 < t < 5

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A: Note that, the parametric equation of a line through the points x0,y0,z0 and parallel to the vector…

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Q: A curve is given by the parametric equations x(t)=t2-4t and y(t)=t2+2t-3. The line tangent to the…

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Q: Find a parametric equation for the line tangent to the curve of the intersection of the surfaces at…

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Q: A curve C has parametric equations x = e' , y =t- Int, where t>0. (i) Show that there is no tangent…

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Q: Suppose parametric equations for the line segment between (7, 8) and (5, 1) have the form: Sx(t) = a…

A: We have to find

Q: (a) By eliminating the parameter, sketch the trajectory over the time interval 0 ≤ t ≤1 of the…

A: Given- x=cosπt, y=sinπt To sketch- (a) The trajectory over the time interval 0 ≤ t ≤1 of the…

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

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Q: a)Find the equation of the tangent line to the curve and find a set of parametric equations for the…

A: To find the tangent equation of the line to the curve of intersection of both the given surfaces at…

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A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…

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

A: Here, the given parametric equation of the curve is: r(t)=(x(t),y(t),z(t)) where x=6et, y=t e2t, z=t…

Q: I Find the Cartesian equation of the curves given by the following parametric equations. b cost,…

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Q: Find parametric equations for the tangent line to the curve of intersection of the paraboloid z = x²…

A: Given :-  The curve of intersection of the paraboloid z = x2 + y2 and the ellipsoid x2 + y2 + z2 =6…

Q: Suppose parametric equations for the line segment between (2, 8) and (– 2, 0) have the for s ¤(t) =…

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Q: Find a parametric description for the curve y=4-x^2 from (-2, 0) to (2, 0) such that t=0 corresponds…

A: Given: The curve y=4-x2 from (-2,0) to (2,0)

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Q: Find a parametric description for the curve x=y^2-9 from (0, 3) to (-5, -2) such that t=0…

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Q: Determine the points where the parametric curve x = t3 -3t, y t3 - 12t have horizontal and vertical…

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Q: Consider the smooth parametric curve C₁ defined by equations t³-t²- 2t Xx y = = (161²- 48t +35) NIW…

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Q: 8. The tangent line to the curve r(t) = Li+ej=t'k 2-t at the point P(1,1, -1) intersects the line…

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Q: Find the parametric equations for the tangent line to the curve x=t^2−1,y=t^4+1,z=t^4 at the point…

A: Given: x=t2-1, y=t4+1, z=t4 Point 8, 82, 81, is for t=3 as you can see substituting it in the three…

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Q: List all of the points (x,y) on the parametric curve x=t^3+4t,  y=6t^2 where the tangent line is…

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Q: 2. Find parametric equations for the tangent line to the curve r(t) = (t8,t³,t7) at (1,1,1).

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Q: 1. A curve in the plane is defined parametrically by: x(t) = t +1 and y(t) = t2-5t +2. a)Convert the…

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Q: 2. Find the parametric equations for the line tangent to the curve given by r(t) = cos ti + sin tj +…

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Q: Suppose parametric equations for the line segment between (3, 1) and (2, 4) have the form: ( x(t) =…

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Q: Select the curve generated by the parametric equations. Indicate with an arrow the direction in…

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Q: Suppose parametric equations for the line segment between (6, 1) and (7, 7) have the form: Sx(t) = a…

A: We have find four unknowns so we need four independent equations.

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

A: Let's find.

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.