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Question
Find the points of discontinuity of f, where `f (x) = {(sinx/x, if x<0),(x + 1, if x >= 0):}`
Solution
`f (x) = {(sinx/x, if x<0),(x + 1, if x >= 0):}`
At x = 0, f (0) = 1
L.H.L. = `lim_(x->0^+) f(x) = lim_(h->0)(sin(-h))/-h = 1`
R.H.L = `lim_(x->0^+) f(x) = lim_(h->0) (h + 1) = 0 + 1 = 1`
`lim_(x->0^-) f(x) = lim_(x->0^+) f (x) = f (0)`
∴ f is continuous at x = 0
When x<0, sinx and x both are continuous ,
∴ `sinx/x` is also continuous.
When x>0, f(x) = x = x + 1 is a polynomial
∴ f is continuous.
= f is not discontinuous at any point.
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