\[\lim_{x \to \infty} a^x \sin \left( \frac{b}{a^x} \right), a, b > 1\] is equal to

b \[\lim_{x \to \infty} a^x \sin \left( \frac{b}{a^x} \right)\]\[ \lim_{x \to \infty} b\left( \frac{\sin \frac{b}{a^x}}{\frac{b}{a^x}} \right)\]\[Let \frac{b}{a^x} = y\]\[x \to \infty \]\[ \therefore y \to 0\]\[ \lim_{y \to 0} \frac{b \sin y}{y} = b\]

Lim X → ∞ a X Sin ( B a X ) , a , B > 1 is Equal to - Mathematics

प्रश्न

$lim_{x \to \infty} a^{x} \sin (\frac{b}{a^{x}}), a, b > 1$ is equal to

पर्याय

b
a
a log_e b
b log_e a

MCQ

उत्तर

$lim_{x \to \infty} a^{x} \sin (\frac{b}{a^{x}})$
$lim_{x \to \infty} b (\frac{\sin \frac{b}{a^{x}}}{\frac{b}{a^{x}}})$
$L e t \frac{b}{a^{x}} = y$
$x \to \infty$
$∴ y \to 0$
$lim_{y \to 0} \frac{b \sin y}{y} = b$

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Concept of Limits - Algebra of Limits

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Q 28 Q 27 Q 29

पाठ 29: Limits - Exercise 29.13 [पृष्ठ ८०]

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आरडी शर्मा Mathematics [English] Class 11

पाठ 29 Limits
Exercise 29.13 | Q 28 | पृष्ठ ८०

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Concept of Limits - Algebra of Limits

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Lim X → ∞ a X Sin ( B a X ) , a , B > 1 is Equal to - Mathematics

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Lim X → ∞ a X Sin ( B a X ) , a , B > 1 is Equal to - Mathematics

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