Use graphs, and tables to find the limit, and identify any vertical asymptotes of the function. Limit of 1 divided by quantity x minus 10^2 as approaches 10 from the left.
The function f(x) = 1/(x - 10)
The table list values of f(x) for several x - values approaches 10 from left.
Observe Table, and Graph:
So, when X approaches 10 from the left (x - 10) is a small negative number. Thus, the quotient 1/(x - 10) is a large negative number and f(x) approaches negative infinity from the left side of the x = 10. Therefore, we can conclude that x = 10 is a Vertical Asymptote of the Graph of f(x) and lim x ----10 f(x) = lim x ---- 10 1/x - 10 = - infinity.
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