Evaluate? #lim/(xrarr0)#(#1/(tsqrt(1+t))-1/t#)
1 Answer
Explanation:
I am assuming that we have:
Since substituting 0 in the place of
We find the LCM between
We see that it is
We now rewrite our function.
=>
=>
Let's try to rationalize the numerator.
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=>
=>
=>
=>
We can now plug 0 in the place of
=>
=>
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=>
That is our answer!
This works because there was a hole in the graph of our original function. Our new one simply traces over that point, making that point defined. If the function was, say, asymptotically discontinuous (and undefined) at a given point, then our trick would not be able to work.