Let f ( t ) 0 x 2 sin 2 x e t x d x , t 0 f ( t ) 0 x 2 sin 2 x e t x d x , t 0 (i) Show that f f is continuous on 0 , ) 0 , ) and twice differentiable on ( 0 , ) ( 0 , ) (ii) Find f and work out the limits lim, f (t) and lim, f' (t) ...

i ii iii Data from theorem 124 a b c Data from theorem 125 ...

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

Question:

Let $f (t) := \int_{0}^{\infty} x^{- 2} \sin^{2} x e^{- t x} d x, t ⩾ 0$ .

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

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

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Measures Integrals And Martingales

ISBN: 9781316620243

2nd Edition

Authors: René L. Schilling

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Question Posted: Jan 25, 2024 01:03 AM

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

Question:

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

Step by Step Answer:

i ii iii Data from theorem 124 a b c Data from theorem 125 ...View the full answer

Measures Integrals And Martingales

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