Question

`f(x) = {{:(x^10 - 1",", if x ≤ 1),(x^2",", if x > 1):}` is discontinuous at

विकल्प

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Answer 1

1

Explanation:

At `x` = 1, L.H.L = `lim_(x -> 1^-) f(x) = (x^10 - 1)` = 0

R.H.L = `lim_(x -> 1^+) = f(x) = lim_(x -> 1^+) (x^2)` = 1

`f(1) = 1^10 - 1` = 0

∴ L.H.L ≠ R.H.L ≠ `f(1)`

⇒ `f` is not continous at `x` = 1.

At `x = C < 1, lim_(x -> C) (x^10 - 1) = C^10 - 1 = f(C)`

⇒ `f` is continuous at all points x ∈ R – |L|

Point of discontinuity is `x` = 1.