The domain the $\ln(x)$ is just positive reals, so the left-hand limit at 0 doesn"t really make sense.
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For a limit to exist, the two borders approaching from the left and also right side require to match up.
I.e. We need $$\lim\limits_x\to0^-\ln(x) = \lim\limits_x\to0^+\ln(x)$$ to it is in true.
Since $\ln(x)$ is not defined for $x\leq 0$ assuming us are assessing over the reals, the left-hand border can"t be evaluated, and also thus the limit does not exist.
If friend are analyzing over the facility numbers, that"s a somewhat various story, yet given her wording, I"ve assumed the we"re talking around the reals here.
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Calculating this limit: $\lim_n\to\infty\;n\cdot\sqrt\frac12\left(1-\cos\frac360^\circn\right)$
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