Find-lim-x-2-x-2-x-1-x-2-

Question Number 207519 by hardmath last updated on 17/May/24

Find : \lim_{x \to 2^{-}} \frac{(x + 2) \cdot (x + 1)}{∣ x + 2 ∣} = ?

Answered by Frix last updated on 17/May/24

f (x) = \frac{(x + 2) (x + 1)}{∣ x + 2 ∣} = {\begin{cases} - (x + 1), x < - 2 \\ (x + 1), - 2 < x \end{cases}

We approach 2 from the negative side but

for 0 < x < 2 we get

\lim_{x \to 2^{-}} (x + 1) = 3

The only discontinuity is at x = - 2

\lim_{x \to - 2^{-}} f (x) = 1 \neq \lim_{x \to - 2^{+}} f (x) = - 1

Commented by hardmath last updated on 18/May/24

answer : 3 professor ?

Commented by Frix last updated on 18/May/24

Yes . x = 2 makes no problem, you can just

insert f (2) = \frac{(2 + 2) (2 + 1)}{∣ 2 + 2 ∣} = \frac{4 \times 3}{4} = 3

Commented by hardmath last updated on 18/May/24

thank you dear professor