InterviewSolution
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InterviewSolution
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`f(x)={{:((sin^(-1))/(x)",","जब",x ne 0),(1",","जब",x = 0):}x = 0` पर सांतत्य की जाँच कीजिए । |
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Answer» (i) `f(0)=1` (ii) `f(0-0)=underset(h rarr 0)(lim)f(0+h)=underset(h rarr 0)(lim)(sin^(-1)(0+h))/(0+h)` `=underset(h rarr d)(lim)(sin^(-1)h)/(h)` `=1," "[because underset(x rarr 0)(lim)(sin^(-1)x)/(x)=1]` (ii) `f(0-0)=underset(h rarr 0)(lim)f(0-h)=underset(h rarr 0)(lim)(sin^(-1)(0-h))/(0-h)` `=underset(h rarr 0)(lim)(sin^(-1)(-h))/(-h)` `=underset(h rarr 0)(lim)(sin^(-1)h)/(-h)," "[because sin^(-1)(-x)=-sin^(-1)x]` `=underset(h rarr 0)(lim)(sin^(-1)h)/(h)," "[because underset(x rarr 0)(lim)(sin^(-1)x)/(x)=1]` =1 `therefore" "f(0-0)=f(0+0)=f(0)` इसलिए फलन f(x) बिन्दु x = 0 पर संतत है । |
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