First slide

Introduction to limits

Question

$If α, β are the roots of a x^{2} + b x + c = 0 then \underset{x \to α}{L t} {(1 + a x^{2} + b x + c)}^{\frac{1}{x - α}} is$

Moderate

A

$a (α - β)$
B

$\log |a (α - β)|$
C

$e^{a (α - β)}$
D

$a (α + β)$

Solution

$G . L = \underset{e^{x \to α}}{L t} (\frac{a x^{2} + b x + c}{x - α}) = \underset{e^{x \to a}}{L t} \frac{a (x - α) (x - β)}{x - α} = e^{a \cdot (α - β)}$

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