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JEE Main202125 Feb 2021Evening ShiftMathematicsLimitsActual

If lim x → 0 a x - e 4 x - 1 a x e 4 x - 1 exists and is equal to b , then the value of a - 2 b is ___ .

Correct answer

0

Step-by-step solution

lim x → 0 a x - e 4 x - 1 a x e 4 x - 1    0 0 = lim x → 0 a x - e 4 x - 1 a x · 4 x Use lim x → 0 e 4 x - 1 4 x = 1 Apply L 'Hospital Rule = lim x → 0 a - 4 e 4 x 8 a x ( a - 4 0 form ) limit exists only when a - 4 = 0 ⇒ a = 4 = lim x → 0 4 - 4 e 4 x 32 x = lim x → 0 1 - e 4 x 8 x       0 0 = lim x → 0 - e 4 x · 4 8 = - 1 2 ⇒ b = - 1 2 a - 2 b = 4 - 2 - 1 2 = 5

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