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Question-149373




Question Number 149373 by fotosy2k last updated on 05/Aug/21
Answered by john_santu last updated on 05/Aug/21
  lim_(x→0) (((1+((3x)/2))−(1+((2x)/2)))/(x(1+2x)))  = lim_(x→0) ((x/2)/x) ×lim_(x→0) (1/(1+2x))= (1/2)×1=(1/2)
$$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left(\mathrm{1}+\frac{\mathrm{3x}}{\mathrm{2}}\right)−\left(\mathrm{1}+\frac{\mathrm{2x}}{\mathrm{2}}\right)}{\mathrm{x}\left(\mathrm{1}+\mathrm{2x}\right)} \\ $$$$=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\frac{\mathrm{x}}{\mathrm{2}}}{\mathrm{x}}\:×\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2x}}=\:\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{1}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$
Commented by fotosy2k last updated on 05/Aug/21
thank you
$${thank}\:{you} \\ $$

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