Please help thank you..
1 answer:
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The linear approximation to 
centered at 
is
What this means is that you can use the tangent line to at to get a decent approximation of at some other value of 
to within a certain degree of accuracy depending on how close this value is close to 
. (Note that when , the approximation is exact; 
.)
So what you're asked to do is find an approximate value of a zero of near 
. That is to say, you're looking for some value 
such that 
, but all you have at your disposal is the linear approximation to the function.
You know that if is a zero of 
, then , so you get
Solving for, you find
This means that an approximate zero of is 
.
What this means is that you can use the tangent line to
So what you're asked to do is find an approximate value of a zero of
You know that if
Solving for
This means that an approximate zero of