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Mathematics - Limits Question with Solution | TestHub

MathematicsLimitsAlgebraic and Rational LimitsMedium2 minPYQ_2015

MathematicsMediumnumerical

Let m and n be two positive integers greater than 1. If $\lim_{α \to 0} (\frac{e^{c o s (α^{n})} - e}{α^{m}}) = - (\frac{e}{2})$ then the value of $\frac{m}{n}$ is

Answer:

2.00

Solution:

$\lim_{α \to 0} \frac{e^{\cos α^{n}} - e}{α^{m}} = - \frac{e}{2}$
$\Rightarrow$ Using L'Hospital's Rule

$\lim_{α \to 0} \frac{e^{\cos (α^{n})} \cdot - \sin (α^{n}) \cdot n α^{n - 1}}{m \cdot α^{m - 1}} = \frac{- e}{2}$
$\Rightarrow \frac{m}{n} = 2$ .

Stream:JEE_ADVSubject:MathematicsTopic:LimitsSubtopic:Algebraic and Rational Limits

⏱ 2mℹ️ Source: PYQ_2015

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