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प्रश्न
Find the value of constant ‘k’ so that the function f (x) defined as
f(x) = `{((x^2 -2x-3)/(x+1), x != -1),(k, x != -1):}`
is continous at x = -1
उत्तर
Given f (x) is continuous at x = -1
`:. f(-1) = lim_(x->-1) f(x)`
`:. k = lim_(x-> -1) (x^2 - 2x -3)/(x+1)`
`= lim_(x->-1) ((x-3)(x+1))/(x+1)` [`∵ x-> -1 => x + 1 != 0`]
= -1-3=-4
∴ K = -4
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