Question Number 213744 by efronzo1 last updated on 15/Nov/24
Answered by golsendro last updated on 15/Nov/24
$$\:\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+\mathrm{4x}\right)^{\frac{\mathrm{3}}{\mathrm{4}}} +\left(\mathrm{1}−\mathrm{4x}\right)^{\frac{\mathrm{3}}{\mathrm{4}}} −\mathrm{2}}{\mathrm{x}^{\mathrm{2}} } \\ $$$$\:\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{3}\left(\mathrm{1}+\mathrm{4x}\right)^{−\frac{\mathrm{1}}{\mathrm{4}}} −\mathrm{3}\left(\mathrm{1}−\mathrm{4x}\right)^{−\frac{\mathrm{1}}{\mathrm{4}}} }{\mathrm{2x}} \\ $$$$\:\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{−\mathrm{3}\left(\mathrm{1}+\mathrm{4x}\right)^{−\frac{\mathrm{5}}{\mathrm{4}}} −\mathrm{3}\left(\mathrm{1}−\mathrm{4x}\right)^{−\frac{\mathrm{5}}{\mathrm{4}}} }{\mathrm{2}} \\ $$$$\:\:=\:−\mathrm{3} \\ $$
Commented by SaifuddinSiam last updated on 15/Nov/24
$$ \\ $$hiiii