Question

$\lim_{x\rightarrow0}f(x), \, का मान ज्ञात कीजिए, जहाँ \,f(x) = \right \begin{cases}{\dfrac{|x|}{x} , \,\,\,\,\,x \neq 0 \\\at0p \atop 0, \, \,\,\,\,\,\,\,\,\,\,\,\, x = 0 \end{cases}$

Answer 1

Answer:

Step-by-step explanation:

$\lim_{x\rightarrow0}f(x), \,f(x) = \right \begin{cases}{\dfrac{|x|}{x} , \,\,\,\,\,x \neq 0 \\\at0p \atop 0, \, \,\,\,\,\,\,\,\,\,\,\,\, x = 0 \end{cases}$

x > 0 के लिए

$R.H.L.=\lim_x_\rightarrow_0^+ f(x)\\\\=\lim_x_\rightarrow_0^+\frac{|x|}{x}\\ \\=\lim_x_\rightarrow_0^+ \frac{x}{x}\\ \\=\lim_x_\rightarrow_0^+ 1\\\\=1$

x < 0 के लिए

$L.H.L.=\lim_x_\rightarrow_0^- f(x)\\\\=\lim_x_\rightarrow_0^-\frac{|x|}{x}\\ \\=\lim_x_\rightarrow_0^- \frac{-x}{x}\\ \\=\lim_x_\rightarrow_0^- (- 1)\\\\=-1$

$\lim_{x\rightarrow0^+}f(x)\neq \lim_{x\rightarrow0^-}f(x)$

अतः  f (x ) का अस्तित्व नहीं है।