InterviewSolution
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InterviewSolution
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k का मान ज्ञात कीजिए यदि फलन x = 0 पर संतत है, जहाँ `f(x)={{:((1-cos 4x)/(8x^(2))",","यदि",x ne 0),(" "k",","यदि",x = 0):}` |
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Answer» (i) `f(0)=k` (ii) R.H.L. `=underset(x rarr 0^(+))(lim)f(x)=underset(h rarr 0)(lim)f(0+h)` `=underset(h rarr 0)(lim)(1-cos 4(0+h))/(8(0+h)^(2))" "[because x = 0 + h ne 0]` `=underset(h rarr 0)(lim)(1-cos 4h)/(8h^(2))` `=underset(h rarr 0)(lim)(2sin^(2)2h)/(8h^(2))` `=underset(h rarr 0)(lim)((sin 2h)/(2h))^(2)` `=1^(2)=1," "[because underset(theta rarr 0)(lim)(sin theta)/(theta)=1]` (iii) L.H.L. `=underset(x rarr 0^(-))(lim)f(x)=underset(h rarr 0)(lim)f(0-h)` `=underset(h rarr 0)(lim)(1-cos 4(0-h))/(8(0-h)^(2))` `=underset(h rarr 0)(lim)(1-cos 4h)/(8h^(2))," "[because cos (-theta)=cos theta]` = 1 चूँकि फलन f(x) बिन्दु x = 0 पर संतत है । `therefore" ""R.H.L.=L.H.L."=f(0)` `rArr" "k = 1` |
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