Good Problem on Limits

If Î±, Î² are the roots of the equation x² + bx + c = 0 then find

lim (1 - cos(x² + bx + c))/(Î² - x)²
x->Î²

2 Answers

106

Asish Mahapatra ·2009-12-08 02:10:48

x²+bx+c = (x-Î±)(x-Î²)

=> lim(xâ†’Î²) 2sin²[(x-Î±)(x-Î²)/2]/(x-Î²)²
= lim(xâ†’Î²)2(x-Î±)²/4

= (Î²-Î±)²/2

(Î±-Î²)²/2

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