What is the limit as x approaches 2 of arctan(((2x^2-8))/(3x^2-6x)) ?

The limit as x approaches 2 of arctan(((2x^2-8))/(3x^2-6x)) is arctan(4/3)

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limit as x approaches 2 of arctan(((2x^2-8))/(3x^2-6x))

x \to 2 lim (arctan (\frac{( 2 x ^{2} - 8 )}{3 x ^{2} - 6 x}))

arctan (\frac{4}{3})

Decimal

0.92729 \dots

Solution steps

x \to 2 lim (arctan (\frac{2 x ^{2} - 8}{3 x ^{2} - 6 x}))

\frac{2 x ^{2} - 8}{3 x ^{2} - 6 x} = \frac{2 ( x + 2 )}{3 x}

= x \to 2 lim (arctan (\frac{2 ( x + 2 )}{3 x}))

Plug in the value

x = 2

= arctan (\frac{2 ( 2 + 2 )}{3 \cdot 2})

\frac{2 ( 2 + 2 )}{3 \cdot 2} = \frac{4}{3}

= arctan (\frac{4}{3})

What is the limit as x approaches 2 of arctan(((2x^2-8))/(3x^2-6x)) ?
The limit as x approaches 2 of arctan(((2x^2-8))/(3x^2-6x)) is arctan(4/3)