(4) Prove that if $n > m > 0$ then \begin{vmatrix} \int_{m}^{n} \frac{\sin t}{t} dt \end{vmatrix} < \frac{4}{m}$. \newline Hence show that $\int_{1}^{\infty} \frac{\sin t}{t} dt$ exists.
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This means that both n and m are positive numbers, and n is greater than m. 2) We want to prove that sin(t) is less than or equal to 4m for all values of t. To do this, we can use the fact that the sine function is bounded between -1 and 1. This means that for Show more…
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