Question

`lim_(x → 0) f(x)` और `lim_(x → 1) f(x)` ज्ञात कीजिए, जहाँ

`f(x) = {(2x + 3, x ≤ 0),(3(x+1), x > 0):}`

Answer 1

`f(x) = {(2x + 3, x ≤ 0),(3(x+1), x > 0):}`

`lim_(x → 0^-) f(x) = lim_(x → 0)[2x + 3] = 2(0) + 3 = 3`

`lim_(x → 0^+) f(x) = lim_(x → 0) 3(x + 1) = 3(0 + 1) = 3`

∴ `lim_(x → 0^-) f(x) = lim_(x → 0^+) f(x) = lim_(x → 0) f(x) = 3`

`lim_(x → 1^-) f(x) = lim_(x → 1) 3(x + 1) = 3(1 + 1) = 6`

`lim_(x → 1^+) f(x) = lim_(x → 1) 3(x + 1) = 3(1 + 1) = 6`

∴ `lim_(x → 1) f(x) = lim_(x → 1^-) f(x) = lim_(x → 1^+) f(x) = 6`