Saved Bookmarks
| 1. |
दर्शाइये कि फलन `f(x) = {{:(x^(3)+3",",x ne 0),(" "1",",x = 0):} x = 0` पर संतत नहीं है । |
|
Answer» (i) `f(0)=1` (ii) R.H.L. `=underset(x rarr 0^(+))(lim)f(x)=underset(h rarr 0)(lim)f(0+h)` `=underset(h rarr 0)(lim)(0+h)^(3)+3," "[because x = 0 + h ne 0]` `=underset(h rarr 0)(lim)h^(3)+3` `=0 + 3 = 3` (iii) L.H.L. `=underset(x rarr 0^(-))(lim)f(x)=underset(h rarr 0)(lim)f(0-h)` `=underset(h rarr 0)(lim)(0-h)^(3)+3" "[because x = 0 - h ne 0]` `=underset(h rarr 0)(lim)(-h)^(3)+3` `= 0 + 3 = 3` `therefore" "underset(x rarr 0^(+))(lim)f(x)=underset(x rarr 0^(-))(lim)f(x) ne f(0)` अत: f(x) बिन्दु x = 0 पर संतत नहीं है । |
|