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lim-x-100-x-100-100-x-1-100-x-DANISH-




Question Number 129723 by Adel last updated on 18/Jan/21
lim_(x→100) [(x^(100) −100^x )(1/(100−x))]=?  DANISH
$$\underset{{x}\rightarrow\mathrm{100}} {\mathrm{lim}}\left[\left(\mathrm{x}^{\mathrm{100}} −\mathrm{100}^{\mathrm{x}} \right)\frac{\mathrm{1}}{\mathrm{100}−\mathrm{x}}\right]=? \\ $$$$\mathcal{DANISH} \\ $$
Answered by bramlexs22 last updated on 18/Jan/21
 lim_(x→100) ((100x^(99) −100^x ln (100))/(−1))   =100^x  ln (100)−100x^(99)
$$\:\underset{{x}\rightarrow\mathrm{100}} {\mathrm{lim}}\frac{\mathrm{100x}^{\mathrm{99}} −\mathrm{100}^{\mathrm{x}} \mathrm{ln}\:\left(\mathrm{100}\right)}{−\mathrm{1}} \\ $$$$\:=\mathrm{100}^{\mathrm{x}} \:\mathrm{ln}\:\left(\mathrm{100}\right)−\mathrm{100x}^{\mathrm{99}} \\ $$
Commented by Adel last updated on 18/Jan/21
with out the Hoopetal Role
$$\mathrm{with}\:\mathrm{out}\:\mathrm{the}\:\mathrm{Hoopetal}\:\mathrm{Role} \\ $$

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