Question
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निर्देश : निम्नलिखित प्रश्नों के लिए निम्नलिखित पर विचार करें:
माना f(x) = |x|2 - |x2| है।
निम्नलिखित कथनों पर विचार कीजिए:
I. f(x), x = 0 पर संतत है।
II. f(x), x = 1 पर संतत है।
ऊपर दिए गए कथनों में से कौन सा/से सही है/हैं?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFव्याख्या:
f(x) = [x]2 - [x2]
x = 0 पर
LHL = \(\rm \lim_h\rightarrow 0\) [0 - h]2 - [(0 - h)2]
= (-1)2 - 0 = 1
RHL = \(\rm \lim_h\rightarrow0 [0 + h]^2 – [(0 + h)^2] \)
= 0 - 0 = 0
LHL ≠ RHL; f(x), x = 0 पर संतत नहीं है
x = 1 पर
LHL = \(\rm \lim_h\rightarrow 0\) [[1 - h]2 - [(1 - h)2]
= 1 - 1 = 0
RHL = \(\rm \lim_h\rightarrow 0\) [1 + h]2 - [(1 + h)2]
= 1 - 1 = 0
⇒ f(x), x = 1 पर संतत है; LHL = RHL।
इसलिए, विकल्प (b) सही है।
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