10. Given the curve C defined by the vector-valued functionF(t) =< cost + sint, cost- sint, t>a) find an equation of the line that is tangent to this curve at the point(1,1,0). (You can give the parametric equations of the line.)b) Find the length of the curve C from the point (1,1,0) to the point.(1,-1,5) (in the direction of increasing t).c) Compute the curvature of the curve C at the point (1,1,0).11. Determine whether the lines L₁ given by x=t, y=1+2t, z=2+ 3t,(with -∞ < t < oo) and L₂ given by x = 3 - 4s, y = 3+2s, z = 2-s,(with -∞ < s <∞o) are parallel, intersect or are skew lines.12. Consider the functionf(x, y) = { 27² if (x, y) = (0,0)1if (x, y) = (0,0)a) Does lim(z,y)+(0,0) f(x, y) exist? Justify your answer.b) Is f continuous at (0,0)? Justify your answer.afc) Compute of (0,0), (0,0), if they exist there. (Hint: You will need touse the limit definition of the partial derivative.)

Answered: Image /qna-images/answer/7af73cf8-b97c-4ec4-8a36-bcca7686f141.jpg

10. Given the curve C defined by the vector-valued function r(t) =< cost + sint, cost - sint,t> a) find an equation of the line that is tangent to this curve at the point (1,1,0). (You can give the parametric equations of the line.) b) Find the length of the curve C from the point (1,1,0) to the point (1,-1,5) (in the direction of increasing t). c) Compute the curvature of the curve C at the point (1,1,0).

10. Given the curve C defined by the vector-valued function r(t) =< cost + sint, cost - sint,t> a) find an equation of the line that is tangent to this curve at the point (1,1,0). (You can give the parametric equations of the line.) b) Find the length of the curve C from the point (1,1,0) to the point (1,-1,5) (in the direction of increasing t). c) Compute the curvature of the curve C at the point (1,1,0).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 22E

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