$25. Find the unit tangent and the principal unit normal vectors for the helix given byr(t)= (2 cos t) i + (2 sin t) j+ tk.6. Find the curvature of r(t)= ti+t2j + t k.7. Find the curvature of the plane y =cos() +e2xat r 0.8. Find the maximum curvature of y In . ck aveerune, chece cleiractieeluvahe +ozors9. Find the tangential component ar and normal component an for the curve given byr(t) 3ti tj+ tk.10. Let a(t) = 2t i + e' j + cos(t) k denote the acceleration of a moving particle. If the initiav(0) = i+ 2j-k, find the particle's velocity v(t) at any time t.V2 x(a) Find the domain of f(x, y)=In(-1)(b) Sketch the graph of f(x, y) = 6 -2y12. Find the limit of show it does not exists.

Question
Asked Jun 12, 2019
51 views

Help with #5

$2
5. Find the unit tangent and the principal unit normal vectors for the helix given by
r(t)
= (2 cos t) i + (2 sin t) j+ tk.
6. Find the curvature of r(t)= ti+t2j + t k.
7. Find the curvature of the plane y =
cos() +e
2x
at r 0.
8. Find the maximum curvature of y In . ck aveerune, chece cleiractie
eluvahe +ozors
9. Find the tangential component ar and normal component an for the curve given by
r(t) 3ti tj+ tk.
10. Let a(t) = 2t i + e' j + cos(t) k denote the acceleration of a moving particle. If the initia
v(0) = i+ 2j-k, find the particle's velocity v(t) at any time t.
V2 x
(a) Find the domain of f(x, y)=In(-1)
(b) Sketch the graph of f(x, y) = 6 -2y
12. Find the limit of show it does not exists.
help_outline

Image Transcriptionclose

$2 5. Find the unit tangent and the principal unit normal vectors for the helix given by r(t) = (2 cos t) i + (2 sin t) j+ tk. 6. Find the curvature of r(t)= ti+t2j + t k. 7. Find the curvature of the plane y = cos() +e 2x at r 0. 8. Find the maximum curvature of y In . ck aveerune, chece cleiractie eluvahe +ozors 9. Find the tangential component ar and normal component an for the curve given by r(t) 3ti tj+ tk. 10. Let a(t) = 2t i + e' j + cos(t) k denote the acceleration of a moving particle. If the initia v(0) = i+ 2j-k, find the particle's velocity v(t) at any time t. V2 x (a) Find the domain of f(x, y)=In(-1) (b) Sketch the graph of f(x, y) = 6 -2y 12. Find the limit of show it does not exists.

fullscreen
check_circle

Expert Answer

Step 1

Given curve: r(t) = (2cost)i + (2sint)j + tk

Recall the expressions for unit tanget and principal unit normal vectors:

  • The Unit Tangent Vector to r(t) at t is T(t) = r'(t) / |r'(t)|
  • The Principal Unit Normal Vector to C at t is N(t) = T'(t) / |T'(t)|

Step 2

Please see the white board for subsequent calculations. Recall the famous rules of differentiation:

  • d(cosx)/dx = - sinx
  • d(sinx)/dx = cosx
  • d(x)/dx = 1

 

help_outline

Image Transcriptionclose

r(t)(2costi(2sin)j+tk r'f)(-2 sin)+(2 cosf)j k

fullscreen
Step 3

Please see the white board for further calculations. Recall the famous ru...

help_outline

Image Transcriptionclose

2 sint)+(2cost) +12 = /4(sin'r+cos't)+1 4+ = 5 r(

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Calculus

Derivative

Related Calculus Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: Hello,  I need help explaining how pi(k)/2 came about, I know where pi/4 came from. Thank you for th...

A: Consider the provided trigonometry equation.

question_answer

Q: This is #1

A: Part (a)Consider an object moving along a line with the velocity and initial position.

question_answer

Q: Find the slope of the secant line between x=2 and x=5 on the graph of the function f(x)=−2x2+2x+3.

A: We have to find  the slope of the secant line between x=2 and x=5 on the graph of the function f(x)....

question_answer

Q: Define R as the region bounded by the graphs of f(x)=x2 +2x+2, x=−2, x=0, and the x-axis. Using the ...

A: Click to see the answer

question_answer

Q: A storage shed is to be built in the shape of a box with a square base. It is to have a volume of 56...

A: Let the length of each side of the base= x feet and the height of the box= y feet. Volume = length *...

question_answer

Q: Find the intervals on which f is increasing and the intervals on which it is decreasing   f(x) = -2 ...

A: First, we find f'(x).

question_answer

Q: Find the area of the region described. -4x and xIn 3 The region bounded by y e. ye X The area of the...

A: We first draw a rough sketch of y=e^x, y=e^-4x and x=ln 3And find the region bounded by them.

question_answer

Q: Graph the following function.  Then use geometry to find the area and net area of the region describ...

A: Graphed the lines first. Area between y=3x-6,x axis and x=8 is above the x -axis (Blue shaded area)....

question_answer

Q: I need help on how to contruct the definite integral needed to find the area of the geometric shape ...

A: Formula of area of triangle is = (1/2)*b*h, where b=base, h=height