The limit of the function as x tends to 2 is 1
Given the function f(X) expressed as;
[tex]f(x)=\frac{\frac{1}{x-1}}{x-1} \\[/tex]
This can also be expressed as:
[tex]f(x) = \frac{1}{(x-1)^2}[/tex]
Assuming the limit of f(x) approaches 2, this means we are to substitute x = 2 into the function as shown
[tex]\lim_{x \to2} \frac{1}{(x-1)^2}\\= \frac{1}{(2-1)^2}\\=\frac{1}{1^2}\\=1[/tex]
This shows that the limit of the function as x tends to 2 is 1
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