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if

[tex]\lim _{x \rightarrow 2 } \frac{f(x)}{x^2-4} = 7 [/tex]

find the limit

[tex]\lim_{x\rightarrow 2 } \frac{f(x)}{x-2 } [/tex]

one of my students answered like this

from the given

[tex]\frac{f(x)}{x^2-4} = 7 \Rightarrow f(x) = 7(x^2-4) [/tex]

then he complete the solution

[tex]\lim_{x\rightarrow 2} \frac{7(x-2)(x+2)}{x-2} = 28 [/tex]

which is true, what he did in this

[tex]\frac{f(x)}{x^2-4} = 7 \Rightarrow f(x) = 7(x^2-4) [/tex]

is not true 100%, it is true around 2

What is your opinion ?

Thanks in advance