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If function `f(x)=x-(|x|)/(x),x lt 0` `=x+(|x|)/(x),x gt 0` `=1,x=0`, thenA. `underset(x to 0^(-))(lim) `f(x) dose not existB. `underset(x to 0^(+))(lim) `f(x) dose not existC. f(x) is continous at x = 0D. `underset(x to 0^(-))(lim) f(x) ne underset(x to 0^(+))(lim) f(x)` |
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Answer» Correct Answer - C Given function, `f(x) = x - (|x|)/(x), x lt 0` `= x + (|x|)/(x), x gt 0 = 1, x = 0` Now, at x = 0 `LHL = underset(x to 0)(lim) f(x) = underset(x to 0^(-))(lim) (x - (|x|)/(x))` `underset(x to 0)(lim) (x - ((-x))/(x)) = underset(x to 0)(lim) (x + 1) = 1` `RHL = underset(x to 0^(+))(lim) f(x) = underset(x to 0)(lim) + (x + (|x|)/(x))` `= underset(x to 0)(lim) (x + 1) = 1` and f(0) = 1 `:. underset(x to 0^(-))(lim) f(x) = underset(x to 0)(lim) f(x) = f(0) = 1` `implies f(x)` is continuous at x = 0 |
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