8. For the curve given by r(t)=√√² +8 i + In(t² + 8)j + tk 2 find: a. r'(t)

Q: Find the points on the curve t² 16t+ 6, y X = = A. a horizontal tangent line B. a vertical tangent…

A: Given the curve is x=t2-16t+6  and y=t2+4t+3

Q: Evaluate [F·dr if F(x, y)=(4e³)ī +(4xe³)j and the curve C' is line segments going from (0,0) to…

A: To evaluate ∫C F⇀·dr⇀ if F⇀x, y=4eyi⇀+4xeyj⇀ and the curve C is line segments from 0, 0 to 5, 4 to…

Q: Find the distance between the point (0, 4, -1) and the line defined by r(t) = +t

A:

Q: b) Evaluate S(2y + 4z)dx + (2æ + 3z)dy + (4x + 3y)dz, where C is the curve given by r(t) = for 0 <t…

A: given ∫C2y+4zdx+2x+3zdy+4x+3ydz where C is the curve given by rt=t3,2sinπt2,3cosπt2 for 0≤t≤1…

Q: Find the length of the curve defined by 2? = 2y3 from x = 0 to x = 4:|| %3|

A:

Q: Find the length of the curve x = 5-t, for 1 < t < 2. length = y = 3-t, z = 3t 5,

A:

Q: 5. Find the length of the curve described by y - x3/2 from x=0 to x=8. 512√2 (C) 15 26 (A) 20 3 (B)…

A:

Q: Sketch the curve r(t)=f°i+tj and indicate the orientation. Find r'(t) and sketch r(1) & r°(1).

A: First we will plot the given parameters.

Q: 4. Find the unit tangent vector T(t) to the curve r(t) = (In(cos t), cost, sin t) at time t. (a)…

A:

Q: Consider the tangent line to the curve r(t) = t2i −(1/(t + 1))j +(4 − t2)k at the point P(4, 1, 0).…

A: Given the tangent line to the curve r→t=t2i^−1t+1j^+4−t2k^  at the point P4,1,0. We have to…

Q: Consider the folloinwg curve: y = square root of -1+2x At what point on the given curve is the…

A: Consider the folloinwg curve: y = square root of( -1+2x) to find the point on the given curve is the…

Q: Find the speed of the curve 7 (t) = (5t2 + + 6, 7t + 1, t³ + 8t) at t = 4 Бpeed

A: Magnitude of the velocity is speed