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Use continuity to evaluate the limit:

\lim_(x \to 2)\arctan((x^2-4)/(3x^2-6x) )

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Find the limit...


\lim_(x \to 2) tan^(-1)((x^2-4)/(3x^2-6x) )

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


\Longrightarrow \lim_(x \to 2) tan^(-1)((x^2-4)/(3x^2-6x) )

Factor the top and bottom of the expression.


\Longrightarrow \lim_(x \to 2) tan^(-1)(((x+2)(x-2))/(3x(x-2)) )

Cancel the common factor "(x-2)."


\Longrightarrow \lim_(x \to 2) tan^(-1)((x+2)/(3x) )

Now plug in the limit.


\Longrightarrow \lim_(x \to 2) tan^(-1)((2+2)/(3(2)) ) \Longrightarrow \lim_(x \to 2) tan^(-1)((4)/(6) )=\boxed{tan^(-1)((2)/(3) )}


\lim_(x \to 2) tan^(-1)((x^2-4)/(3x^2-6x) )=\boxed{\boxed{tan^(-1)((2)/(3) )}} \therefore Sol.

Thus, the limit is solved.

User Binji
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