# 10. Let a(t) = 2ti + e'j+ cos(t) k denote the acceleration of a moving particle. If the initial velocity isv(0) i+2j-k, find the particle's velocity v(t) at any time t.2-x(a) Find the domain of f(x, y) = In(a-1)(b) Sketch the graph of f(r, y) 6-x2y.12. Find the limit of show it does not exists.4(a)lim(ay)(0,0) 2 + ysxy y(b)lim(ay)(1,0) ( 1)2 +y2ve, then the arc length is always increasing, so s' (t)> 0 for t> a. Last, if= 1 for all t, thens()Il r'(u) du =h means that t represents the arc length as long as a =0.-da1 du = t - a,

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Step 1

The acceleration of the moving particle is given by,

a(t)=2ti+etj+cos(t)k

To find the velocity at time instant t, integrate a(t) with respect to t.

Step 2

Where C is the integration constant.

since initial velocity is v(0)=i+2j-k.

substitute i+2j-k for v(t) and 0 for t in equation 1.

Step 3

Substitute i+j-k for C...

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