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lim-x-pi-picos2x-1-1-cosx-




Question Number 169148 by mathlove last updated on 25/Apr/22
lim_(x→π) ((πcos2x−1)/(1+cosx))=?
$$\underset{{x}\rightarrow\pi} {\mathrm{lim}}\frac{\pi{cos}\mathrm{2}{x}−\mathrm{1}}{\mathrm{1}+{cosx}}=? \\ $$
Commented by infinityaction last updated on 25/Apr/22
     p =   ((πcos 2π−1)/(1+cos π))        p  =  ((π×1−1)/(1−1)) = ((π−1)/0) = ∞
$$\:\:\:\:\:{p}\:=\:\:\:\frac{\pi\mathrm{cos}\:\mathrm{2}\pi−\mathrm{1}}{\mathrm{1}+\mathrm{cos}\:\pi} \\ $$$$\:\:\:\:\:\:{p}\:\:=\:\:\frac{\pi×\mathrm{1}−\mathrm{1}}{\mathrm{1}−\mathrm{1}}\:=\:\frac{\pi−\mathrm{1}}{\mathrm{0}}\:=\:\infty \\ $$$$ \\ $$
Commented by mathlove last updated on 25/Apr/22
way πcos2x−1≠π(cos2x−1)
$${way}\:\pi{cos}\mathrm{2}{x}−\mathrm{1}\neq\pi\left({cos}\mathrm{2}{x}−\mathrm{1}\right) \\ $$

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