Question Number 222829 by hardmath last updated on 08/Jul/25
![If f(x) = ((3x + [x])/(2x)) Find lim_(x→−5^+ ) f(x) − lim_(x→−5^− ) f(x) = ?](https://www.tinkutara.com/question/Q222829.png)
$$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{3x}\:+\:\left[\mathrm{x}\right]}{\mathrm{2x}} \\ $$$$\mathrm{Find}\:\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow−\mathrm{5}^{+} } {\mathrm{lim}}\:\mathrm{f}\left(\mathrm{x}\right)\:−\:\underset{\boldsymbol{\mathrm{x}}\rightarrow−\mathrm{5}^{−} } {\mathrm{lim}}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:? \\ $$
Answered by mehdee7396 last updated on 08/Jul/25
![((3(−5)+[−5^+ ])/(2(−5)))−((3(−5)+[−5^− ])/(2(−5))) =((−15−5)/(−10))−((−15−6)/(−10))=−(1/(10))](https://www.tinkutara.com/question/Q222831.png)
$$\frac{\mathrm{3}\left(−\mathrm{5}\right)+\left[−\mathrm{5}^{+} \right]}{\mathrm{2}\left(−\mathrm{5}\right)}−\frac{\mathrm{3}\left(−\mathrm{5}\right)+\left[−\mathrm{5}^{−} \right]}{\mathrm{2}\left(−\mathrm{5}\right)} \\ $$$$=\frac{−\mathrm{15}−\mathrm{5}}{−\mathrm{10}}−\frac{−\mathrm{15}−\mathrm{6}}{−\mathrm{10}}=−\frac{\mathrm{1}}{\mathrm{10}} \\ $$