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Numerade Educator

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Problem 74 Hard Difficulty

In Exercises $71 - 74 ,$ complete the following tables and state what you believe $\lim _ { x \rightarrow 0 } f ( x )$ to be.
$$\begin{array} { c | c c c c c } { x } & { - 0.1 } & { - 0.01 } & { - 0.001 } & { - 0.0001 } & { \dots } \\ \hline f ( x ) & { ? } & { ? } & { ? } & { ? } \end{array}$$
$$\begin{array} { c c c c c } { \text { (b) } } & { 0.1 } & { 0.01 } & { 0.001 } & { 0.0001 } & { \ldots } \\ \hline f ( x ) & { ? } & { ? } & { ? } & { ? } \\ \hline \end{array}$$
$$f ( x ) = x \sin ( \ln | x | )$$

Answer

a) 0
b) 0

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Video Transcript

questions. Seventy four asked you to complete the falling tables and state where you believe limit of f of X as X approaches. Zero. To be part A. Is this table right here? And if you plug it in to the calculator, we're going to get thes. Falling values will get. Paz is zero point zero seven four negative point zero zero nine nine six times ten to the negative fourth power and two times ten to the negative Fifth Power Party is exact, saying said the's time. The X follows a positive. So the values being negative point zero seven four positive pointers or nine nine negative six times ten to negative fourth power and negative two times ten to negative fifth power. So the limit of f of X as X approaches zero from the left, which these values are will be zero and the limit of f of X as extra push zero from the right, which these values are. It would also be zero. Therefore, we can conclude that the limit has except push zero of f of x zero as well