2. Find the parametric equations for the line tangent to the curve given by r(t) = cos ti + sin tj + tk at the point (0, 1, 7/2). Find the unit tangent vector to the curve at this point.

Q: A curve is defined by the parametric equations x = sint, y = 1– cos t, 0 <t< 27.

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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: Find the slope of the tangent line to the parametric equations: x = 3t2 - 3, y = 2t + 1 at t = 1. %D…

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

A: The given curve is rt=t2+1,4t12,et2-t. Notice that the given curve satisfies t=1(If t=1 is plugged…

Q: Find parametric equations for the line tangent to the helix

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Q: Consider the smooth parametric curve 6 defined by the equations t (t²-3) { 3 (t²- 3)' = = where t€…

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Q: Find the equation of the line tangent to the parametric curve (pictured below) defined by I=, y=t+t…

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Q: Find the equation of the tangent line(s) to the following set of parametric equations at the given…

A: The equation of a line can be obtained by using the expression y-y1=m(x-x1). Here, m is the slope of…

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

A: given parametric equations are x=1+12t , y=t3-t , z=t3+t

Q: Find the parametric equations for the tangent line to the curve æ = t3 – 1,y = to +1, z = t° at the…

A: Find the tangent vector r't:                 r(t)=(t3-1)i +(t5+1)j +t5k Differentiate r(t):…

Q: 5. Find the parametric equations of the line tangent to the curve C defined by the vector equation…

A: To find the parametric equation of the given tangent to the curve. The vector equation of the curve…

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

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Q: Find the unit tangent vector to the curve defined by r(t) = (4 cos(t), 4 sin(t), 2 sin²(t)) π at t =…

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Q: Find the parametric equations of the tangent line LT to the curve C:r (t) = 2 cos(t)i + sin(t)j +…

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

A: Given:

Q: 9/Find Parametric equations for the Line that is tangent to the curve r(t) = eti + (Sint)j + In…

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Q: 3. Consider the parametric equations x = 1+ cos(t), y = -2+ sin(t), 0sts2M. 3.1. Find an equation…

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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: Determine the exact length of the curve for the parametric equation x = tsint and y = tcost for 0 ≤…

A: To find the exact length (arc length) of the curve for the parametric equation x=t sin(t), y=t…

Q: Find parametric equations for the line that is tangent to the curve r(t) = e^t i + (sin t)j + ln (1…

A: The given curve is Differentiating with respect to t, we get Now, we find r(0) and r'(0) and

Q: Find the unit tangent vector to the curve defined by 7(t) = (4cos(t), 4sin(t), 3 sin (t)) at t = 4…

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Find the parametric equations of the tangent line LT to the curve C:r(t) = 2 cos(t)i + sin(t)j+ 2tk…

A: A parametric equation of a curve is given by: C: r(t) = 2cos(t)i + sin(t)j + 2tk Now, we have to…

Q: 3. Find the second derivative for the following set of parametric equations a. x = sqrt(t) , y = 2t…

A: We have to find te second derivative.

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: find the equations of the tangent and normal to the curve expressed in parametric form at the point…

A:

Q: Find the unit tangent vector to the curve defined by 7(t) = (2 cos(t), 2 sin(t), 3 sin²(t)) at t =…

A: Given,           r→t=&lt;2cost , 2sint , 3sin2t&gt; at t=π

Q: 1. Find the second derivative of the parametric equations x = a cos t and y = b sin t 2. Use second…

A:

Q: 1. Eliminate the parameter to find a Cartesian equation of the curve given parametrically by (x(t),…

A: Recall: sin2t+cos2t=1

Q: 10b. Find the parametric equations of the tangent line to the curve at t =1.

A: Given: The position vector is of a particle in space at a time t : r→(t)=&lt;t+1,t,1t&gt;=&lt;x, y,…

Q: Find the parametric equations for the tangent line to the curve x =t* _ 1,y=t* +1,z=t* - at the…

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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: 6. Find a set of parametric equations for the line tangent to the space curve at the given point. 2…

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Q: Consider the curve described by the parametric equations ¤ = t² +4 and y = 3t + 4t. Determine the…

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Q: Find parametric equations for the line tangent to the helix r(t) =(sqrt(2)cos t)i + (sqrt(2) sin t)j…

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Q: 8. Given the vector r(t) = (sint,cos?, In(cos?)), find the equation of the tangent line in…

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Q: B) Find parametric equations for the line that is tangent to the curve r(t) = e'i + (sin t)j + In(1…

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Q: x = +4r2 +4t +1 y =1+3 at the point P(1, 1).

A:

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: Find the parametric equations for the tangent line to the curve x=t^4−1, y=t^3+1, z=t^2 at the point…

A: Consider the given curves and points.

Q: 9.) a. Find the parametric equations for the tangent line to the Curve at' the Specific point. X =t°…

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Q: A curve is defined by the parametric equations T = sin t, y = 1 – cos t, 0<t< 27.

A: Given parametric equations is x = sin t; y = 1 - cos t, 0 ≤t≤2π b) Eliminate t and determine what…

Q: ) Find the equation of the tangent line (in terms of x and y) to the parametric curve at the given…

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

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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

Q: Find the unit tangent vector to the curve defined by 7 (t) = (3 cos (t), 3 sin(t), 5 sin (t)) at t =…

A: we have  r→(t)=3cos(t),3sin(t),5sin2(t) at t=2π3we have to find T→2π3=?and parametric form of…

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

A: Let's find.

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

A:

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.