Question

$\lim_{x\rightarrow5}f(x), \,ज्ञात कीजिए, जहाँ \,f(x) = |x| - 5$

Answer 1

Answer:

Step-by-step explanation:

$\lim_{x\rightarrow5}f(x) ,f(x) = |x| - 5$

$\lim_{x\rightarrow5}f(x)=\lim_{x\rightarrow5}(|x|-5)$

x = 5 - h रखने पर

$\lim_{h\rightarrow0^-}(|5-h|-5)\\\\=\lim_{h\rightarrow0^-}(5-h-5)\\\\=\lim_{h\rightarrow0^-}(-h)\\\\=0$

तथा $\lim_{x\rightarrow5^+}f(x) =\lim_{x\rightarrow5^+} (|x| - 5)$

x = 5 + h रखने पर

$=\lim_{h\rightarrow0^+}(|5+h|-5)\\\\=\lim_{h\rightarrow0^+}(5+h-5)\\\\=\lim_{h\rightarrow0^+}(h)\\\\=0$

$\lim_{x\rightarrow5}f(x)=0$