# \$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.

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Help with #5 help_outlineImage 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
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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

Step 3

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

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