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Question Number 190347 by mustafazaheen last updated on 01/Apr/23
$${how}\:{is}\:{solution} \\ $$$$\underset{{x}\rightarrow\mathrm{sin}\pi\:} {\mathrm{lim}}\frac{\mathrm{sin}\frac{\pi}{\mathrm{2}}}{\mathrm{sin}{x}}=? \\ $$
Answered by JDamian last updated on 01/Apr/23
$${L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{sin}\:{x}}\:=\:\begin{cases}{+\infty\:\:\:{x}\rightarrow\mathrm{0}^{+} }\\{−\infty\:\:{x}\rightarrow\mathrm{0}^{−} }\end{cases} \\ $$$$\nexists\boldsymbol{{L}} \\ $$