Calculate lim (x-2)/(x^2-4), x->2.

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lim (x-2)/(x^2-4), x->2

first we find the function value when x = 2

then (2-2)/(4-4) = 0/0

0/0 means that the substitution methid failed becase both upper and lower functions has a the same root (2)

Now we try to factor the function to try and eleminate the common factor

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lim (x-2)/(x^2-4), x->2

first we find the function value when x = 2

then (2-2)/(4-4) = 0/0

0/0 means that the substitution methid failed becase both upper and lower functions has a the same root (2)

Now we try to factor the function to try and eleminate the common factor

==> (x-2)/(x-2)(x+2) = 1/(x+2)

then lim 1/(x+2)  when x--> 2 is 1/(2+2) = 1/4

then lim (x-2)/(x^2-4), x->2  equals 1/4

 

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