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The way I was thought to approach this type of question was to have a discussion in you head as to what would happen if you substituted numbers that were close to 10.
But they want is to use graphs and tables.
here check this out https://www.symbolab.com/solver/limit-calculator/%5Clim_%7Bx%5Cto10%7D%5Cleft(%5Cfrac%7B1%7D%7B%5Cleft(x-10%5Cright)%5E%7B2%7D%7D%5Cright)/?origin=button
So the limit is positive infinity and there is no vertical asymptote?
There is a vertical asymptote.
But the limit is positive infinity
the vertical asymptote is at 10
The rule for a vertical asymptote in calc is when the limit as x approaches a constant like 10, and the solution is either negative or positive infinity then there is a vertical asymptote at x=10
Also, a vertical asymptote can be defined if it meets the conditions I mentioned above from, at least, ONE SIDE. For example, you only need to test proxy values of x from one side (positive or negative to 10) in order to classify x=10 as a vertical asymptote.
(positive or negative approaching 10)*
|dw:1437971769260:dw| That is one way you could represent it with a table.