Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = V t2 + 15, y = = In(t² + 15), z = t; (4, In(16), 1) (x(t), y(t), z(t)

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A:

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A: formula:

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

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

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

A: Given:

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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…

A:

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A: Given:

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Q: 6. A particle at (1,0,0) starts moving in space in such a way that its position vector at any time t…

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

A:

Q: 4) Find the critical points of the parametric equations x = t* – 1 y = t3 -t

A: Topic:- application of derivatives

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

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Q: Find the First and Second derivatives of y with respect to x from parametric equations. a). x=3 (t…

A: x = 3 t + 22   and y = 9 t2 - 5⇒dxdt = 3 ×2 ×( t + 2)  , dydt = 18 t        Hence dydx = 18 t 6 ( t…

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Q: 4. Find the parametric equations for the tangent line to the curve of intersection of the y z 1…

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A:

Q: Find the 1st and 2nd derivatives of y with respect to x from parametric equations. a). x=3 (t + 2)…

A: First differentiate x and y wrt t then divide

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Q: 8. Solve for the critical points of the parametric equations x = t3 – 1,y = t² +t %3D

A: The answer is found in step-2.

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A:

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A:

Q: 1 '1+t²⁹ Given R'(t) = (4e²t, , 2cosh t), and R(0) = (1, -2,3).

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A:

Q: 11. C is the curve F(t) = (In (2 – t), V+3). Find parametric equations for the tangent line to C at…

A: According to question,Given Curve C,Ft = ln2-t, 1t-2, t+3

Q: 8. Solve for the critical points of the parametric equations x = t - 1,y = t² +t

A: To find the critical points of parametric curve x(t)=t2-1, y(t)=t2+t

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A:

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: 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: 30. Find parametric equations for the tangent line to the curve of intersection of the cone z = x +…

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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:

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.