Let f ( t ) : = 0 x 2 sin 2 x e

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Let f(t):=0x2sin2xetxdx,t0.

(i) Show that f is continuous on [0,) and twice differentiable on (0,).

(ii) Find f" and work out the limits lim, f (t) and lim, f' (t).

(iii) Use (i) and (ii) to obtain a simple expression for f.

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