The value of a , so that lim x → 0 1 x 2 e a x - e x - x = 3 2 , is

We have, lim x → 0 1 x 2 e a x - e x - x = 3 2 ⇒ lim x → 0 a e a x - e x - 1 2 x = 3 2 (using L 'Hospital rule to the left hand side) As x → 0 , the denominator is zero and as the value of the limit is finite so, numerator must be zero for x → 0 . Hence, a - 1 - 1 = 0 ⇒ a = 2 .

Mathematics - Limits Question with Solution | TestHub

MathematicsLimitsGeneral ( Limit existence)Medium2 minPYQ_2018

MathematicsMediumsingle choice

The value of $a$ , so that $\lim_{x \to 0} \frac{1}{x^{2}} (e^{a x} - e^{x} - x) = \frac{3}{2}$ , is

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Answer:

Solution:

We have,

$\lim_{x \to 0} \frac{1}{x^{2}} (e^{a x} - e^{x} - x) = \frac{3}{2}$

$\Rightarrow \lim_{x \to 0} (\frac{a e^{a x} - e^{x} - 1}{2 x}) = \frac{3}{2}$ (using $L$ 'Hospital rule to the left hand side)

As $x \to 0$ , the denominator is zero and as the value of the limit is finite so, numerator must be zero for $x \to 0$ .

Hence, $a - 1 - 1 = 0 \Rightarrow a = 2$ .

Stream:BITSATSubject:MathematicsTopic:LimitsSubtopic:General ( Limit existence)

⏱ 2mℹ️ Source: PYQ_2018

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