lim x->-∞ arctan( |9- 4x^2| / 3 - 4x^2 - 4x )
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Limit Calculator - eMathHelp
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atan ( abs (9- 4x^2) /( 3 - 4x^2 - 4x) )
In rectangle Find the limit at
type
inf
then click option
CALCULATE
You will see solution step by step.
I'll give you an explanation of the last step in the calculation because it can be confusing the way it's written.
( 4 ( - 4 + 3 ( 0 ) )⁻¹ ) =
4 • ( - 4 + 3 • 0 )⁻¹ =
4 • ( - 4 + 0 )⁻¹ = 4 • ( - 4 )⁻¹
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Remark:
a⁻ⁿ = 1 / aⁿ
so
( - 4 )⁻¹ = 1 / - 4¹ = 1 / - 4 = - 1 / 4
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4 • ( - 4 )⁻¹ = 4 • ( - 1 ) / 4 = - 1
atan ( 4 ( - 4 + 3 ( 0 ) ) ⁻¹ ) =
atan ( - 1 ) = - π / 4
3 - 4x^2 - 4x = -(4x^2+4x-3) = -(2x-1)(2x+3)
so now we have
|(2x+3)(2x-3)|/(-(2x+3)(2x-1)) = -|2x-3|/(2x-1)
lim(x→-∞) = -1
and arctan(-1) = -π/4