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Let's do one more example of estimating a limit numerically from a table. So, here we
have the function sine of x over x and we want to estimate the limit as x goes to zero
by plugging in nearby numbers. So, to save ourselves a little bit of time, I've gone
ahead and calculated the function values using a calculator. So, you'll see that in the left
hand column we have some x values and these x values are getting closer and closer to
zero. I have .1, .01, and .0001. And then the right hand column I have the associated
function values. So, one tip really quick. When you are plugging these into your calculator
to evaluate them, make sure you're using radian mode. So, these are the values I get if I
plug these x values into the function. So, let's try to estimate the limit. As x gets
closer and closer to zero, what does it appear that the function values are approaching?
Well, to me it looks like they're approaching one. So, I'm going to estimate that this limit
equals one. And just to remind you that this is just an estimate, I'm going to put that
out to the side. We can never know for sure just by looking at the table. So let's also
just look at the graph just to check and see if our estimate is in fact correct in this
case. Here's a graph of the function, sine of x over x. And it looks like in this case
that our estimate was correct. From the graph we can see that the limit as x goes to zero
of the function is indeed one.