If α is a repeated root of ax2 + bx + c = 0, then Limx→α tan(ax2 + bx + c) / (x - α)2 is ???

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Grade Upto college levelDifferential Calculus

If α is a repeated root of ax²+ bx + c = 0, then Lim_x→αtan(ax² + bx + c) / (x - α)² is ???

Mainak Chakraborty

16 Years agoGrade Upto college level

1 Answer

Badiuddin askIITians.ismu Expert

16 Years ago

Dear Mainak

α is a repeated root of ax²+ bx + c = 0

so ax²+ bx + c=a(x-α)²

now Lim_x→αtan(ax² + bx + c) / (x - α)²

=Lim_x→α[tana(x-α)² ]/ (x - α)²

=Lim_x→αa[tana(x-α)² ]/ a(x - α)²

=a because Lim_x→0tanx /x = 1

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