Let a , b be real numbers such that lim x → 1 x 2 + a x + b [ log ( 2 − x ) ] 2 = 1 . Then

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Mathematics - Limits Question with Solution | TestHub

MathematicsLimitsValue of unknownHard2 minQB

MathematicsHardmultiple choice

Let $a, b$ be real numbers such that $lim_{x \to 1} \frac{[ log ( 2 - x ) ] ^{2}}{x ^{2} + a x + b} = 1$ . Then

Options:(select one or more)

Answer:

B, C

Solution:

The numerator vanishes to second order at $x = 1$ , so $1 + a + b = 0$ and $2 + a = 0$ . Consequently $a = - 2$ and $b = 1$ ; numerator and denominator are both asymptotic to $(x - 1)^{2}$ .

Stream:JEESubject:MathematicsTopic:LimitsSubtopic:Value of unknown

⏱ 2mℹ️ Source: QB

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