The value of limx→∞100xsinx+99sinxx, where [ ] represents the greatest integer function, is

∀x>0;xsinx>1 and ∀x 1 and sinxx 100 and 99sinxx<99100xsinx=100,99sinxx=98

The value of limx→∞100xsinx+99sinxx, where [ ] represents the greatest integer function, is

∀x>0;xsinx>1 and ∀x 1 and sinxx 100 and 99sinxx<99100xsinx=100,99sinxx=98

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$The value of \lim_{x \to \infty} \{[\frac{100 x}{\sin x}] + [\frac{99 \sin x}{x}]\}, where [] represents the$ greatest integer function, is

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$\forall x > 0; \frac{x}{\sin x} > 1 a n d \forall x < 0; \frac{\sin x}{x} < 1$

$\begin{array}{l} \frac{x}{\sin x} > 1 and \frac{\sin x}{x} < 1 \\ \Rightarrow \frac{100 x}{\sin x} > 100 and \frac{99 \sin x}{x} < 99 \\ [\frac{100 x}{\sin x}] = 100, [\frac{99 \sin x}{x}] = 98 \end{array}$

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The value of limx→∞100xsinx+99sinxx, where [ ] represents the greatest integer function, is

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$The value of \lim_{x \to \infty} \{[\frac{100 x}{\sin x}] + [\frac{99 \sin x}{x}]\}, where [] represents the$ greatest integer function, is