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Question
If `f(x) = {{:(x + 2",", x ≤ - 1),(cx^2",", x > -1):}`, find 'c' if `lim_(x -> -1) f(x)` exists
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Solution
Given, `f(x) = {{:(x + 2",", x ≤ - 1),(cx^2",", x > -1):}`
L.H.L = `lim_(x -> -1^-) f(x)`
= `lim_(x -> -1^-) (x + 2)`
= `lim(h -> 0) (-1 - h + 2)`
= `lim_(h -> 0) (1 - h)` = 1
R.H.L = `lim_(x -> 1^+) cx^2`
= `lim_(h -> 0) c(-1 + h)^2` = c
Since the limits exist.
∴ L.H.L = R.H.L
∴ c = 1
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