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Below is an "oracle" function. An oracle function is a function presented interactively. When you type in an $x$ value, and press the --f--$>$ button and the value $f(x)$ appears in the right hand window. There are three lines, so you can easily calculate three different values of the function at one time.

x f(x)

Note: The computer will round your inputs above to $12$ places and will return the function value at the rounded $x$-value.
For example, entering $0.9999999999999$ will result in the computer checking the function at $x = 1$ and returning exactly $f(1)$ rather than a number necessarily near $f(x)$ as $x \rightarrow 1^{-}$.

Determine the limits for the function $f(x)$ as $x$ approaches $0.85$.

$\displaystyle \lim_{x\to 0.85^{-} } f(x)$ =

$f(0.85)$ =

$\displaystyle \lim_{x\to 0.85^{+} } f(x)$ =

Are all of these values the same? . If so then the function is continuous at $0.85$

Are the left and right limits the same at $0.85$? . If so then this function is almost continuous and could be made continuous by redefining one value of the function namely $f(0.85)$.

You can earn partial credit on this problem.