# 9. Find the tangential component aT and normal component aN for the curve given byr(t) 3ti - tj + tk.10. Let a(t) 2ti + e'j+ cos (t) k denote the acceleration of a moving particle. If the initialv(0)= i+2j- k, find the particle's velocity v(t) at any time t.V2-xIn(-1)(a) Find the domain of f (x, y)H(b) Sketch the graph of f(x, y) = 6-x-2y.Find the limit of show it does not exists.4(a)lim(x,y)(0,0) y8(b)ry ylim1)2 +y(a.y)(1,0) (cu ve, then the arc length is always increasing, so s' (t)> 0 for t > a. Last, if)= 1 for all t, thenst) Il r'(u) l du =sents the arc length as long as a = 0a1 du = t- a,

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Help with #9

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Step 1

For a given curve r(t), the tangential component aT and the normal component aN are given by expressions shown on the white board. We therefore need to find:

• r'(t) and |r'(t)|
• r''(t)
• r'(t).r"(t)
• r'(t) x r''(t)
• |r'(t) x r''(t)|
Step 2

Please see the white board for some of the intermediate calculations.

Step 3

Please see white board for so...

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