Question

$\lim_{x\rightarrow0}f(x), \,ज्ञात कीजिए, जहाँ \,f(x) = \right \begin{cases}{\dfrac{x}{|x|} , \,\,\,\,\,x \neq 0 \\\atop \atop 0, \, \,\,\,\,\,\,\,\,\,\,\,\, x = 0 \end{cases}$

Answer 1

Answer:

Step-by-step explanation:

$\lim_{x\rightarrow0}f(x),f(x) = \right \begin{cases}{\dfrac{x}{|x|} , \,\,\,\,\,x \neq 0 \\\atop \atop 0, \, \,\,\,\,\,\,\,\,\,\,\,\, x = 0 \end{cases}$

सीमा $x\rightarrow0$ i.e.   $x\rightarrow0^-$ तथा  $x\rightarrow0^+$

अब  $x\rightarrow0^-=\lim_x_\rightarrow_0_{^-}\frac{x}{|x|} =-1$

तथा $x\rightarrow0^+=\lim_x_\rightarrow_0_{^+}\frac{x}{|x|} =1$

अर्थात  $\lim_{x\rightarrow0}f(x)$  का अस्तित्व नहीं है।