Let 7 (t) = (3t2 – 1,t? – 2t3, Find the line (L) tangent to r(t) at the point (11, – 12, – 64) – 4t4). L:(r, y, z) +t

Q: Let r¡(t) = (-4,0, –5) + t(0, 1, –3) and r2(s) = (2, –2, 10) + s(2,0, 3). Find the point of…

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Q: The skope intercept bm of teine with skope egal to 20 and yirteroept (0, 4) Dy - 2x - 36 -0

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Q: Find all points on the graph of x2y − 2x + 63y = 2 where the tangent line is horizontal. (Enter…

A: Differentiate the equation x2y-2x+63y=2 wrt x:  ddxx2y-ddx2x+ddx63y=ddx22xy+x2dydx-2+63dydx=0

Q: Let 7(t) = (- 2t³ – 3, t2 + t, - 4t2). Find the line (L) tangent to 7 (t) at the point (- 19, 12, –…

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Q: Find the shortest distance between the line L1:2x + y - 3 = 0 and the plane P1:3x - 4y + 12z + 5 =…

A: The formula for the distance between a point and a plane must be used to determine the shortest…

Q: No3. Problem Find the parametric equations for the line through P(-3,2, –3) and Q(1, –1, 4).

A: we only solve one problem at atime so please submit them one by one

Q: Find the distance from the point S(0,0,12) to the line L: x = 4t , y = -2t z = 2t 3

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Q: 5. Evaluate - xy+3z)ds where C is the line starting at (1,1,1) and ending at (-1,-2,-3).

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Q: Evaluate ▼ (x² y + x y z²) ·dr where C is the line segment from ( 1, – 1,0) to (2,1,3 Select one: a.…

A: Given integral is

Q: Consider the function z = ƒ(x, y) = 9x3 - 8x2y + 4y3.;Find dz.

A: Consider the given function, z=fx,y=9x3-8x2y+4y3 The formula of the total derivative dz is,…

Q: Find the distance from the point (-6,-2,0) to the line a(t) = ( – 1, – 2, – 5)t + (3, – 6, 6)

A: We  use the definitions

Q: Find the length of the line given by r(t) = ⟨t, 2t⟩, for a ≤ t ≤ b.

A: To determine: The length of the line given by rt=<t,2t> for a≤t≤b

Q: Find the points on the curve z t? – 10t – 8, y = t² + 4t + 6 that have: A. a horizontal tangent line…

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you.  If…

Q: Find the intersection of the plane x - X = y = - 4y - 5z = -137 and the line r(t) = (5, −5, −4)t +…

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Q: Let F(t) = (-3t² - 1, t³ – 5tª, – 3t²). Find the line (L) tangent to r(t) at the point (-4,-4, − 3)…

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Q: Find the length of the curve 6t, t2, 13 0 st s1 r(t)

A: Given:

Q: Find the length of the curve r(t) (1,t²,), 0sts1 %3D «3 Ost<1

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Q: find point b (x,y) given that M (7,3) is the midpoint of line A(10,4) and b

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Q: Let r(t) = (-5t³ – 1, t² + 5t³, 3t²). Find the line (L) tangent to (t) at the point (39, -36, 12)

A: r→(t)=⟨−5t3−1,t2+5t3,3t2⟩Find the line (L) tangent to r→(t) at the point (39,−36,12)

Q: Find the point P where the line x = 1 + t, y = 2t, z = -3t intersects the plane x + y - z = 0. -000…

A: The objective of this question is to find the point of intersection between a given line and a…