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I need help in the following question:

Let $$f(x) = \left\{\begin{array}{ll} \frac{\sin (0.19x)}{x} &\text{when }x\neq 0\\ L&\text{when }x=0 \end{array}\right.$$

Find the value of $L$ so that $f(x)$ is continuous at 0.

Any comments or advice will be much appreciated.

Thanks.

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    Please note: the backslash to indicate division is ambiguous without parenthesis. When you write `sin 0.19x/x`, the *standard* interpretation is that the division goes before the sine, so you would be telling us that you are looking at $$\sin\left(\frac {0.19x}{x}\right)$$which is probably *not* what you are actually looking at. You would want to write `(sin 0.19x)/x` to describe $$\frac{\sin(0.19x)}{x}.$$But it will be much better if you learn a little bit of $\LaTeX$ and mark-up your posts. Thank you.2012-03-14

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