Question

Evaluate the limit of the function if exist at x = 1 where, f(x) = `{(7 - 4x, x < 1),(x^2 + 2, x ≥ 1):}` 

Answer 1

f(x) = 7 – 4x : x < 1
= x² + 2 : x ≥ 1
`lim_(x -> 1^-) "f"(x) = lim_(x -> 1^-) (7 - 4x)`

= 7 –  4(1)
= 3
`lim_(x -> 1^+) "f"(x) = lim_(x -> 1^+) (x^2 + 2)`

= (1)² + 2
= 3
∴ `lim_(x -> 1^-) "f"(x) = lim_(x -> 1^+) "f"(x)`

∴ `lim_(x -> 1) "f"(x)` exists.

∴ `lim_(x -> 1) "f"(x)` = 3