Question

Está certo essa maneira que eu provei o limite através da definição?​

Lim (2x + 1) = 9
x → 4

| f(x) - L | < ε
| 2x + 1 - 9 | < ε
| 2x - 8 | < ε
| 2 . (x - 4) | < ε
2 . |x - 4 | < ε
|x - 4| < ε/2

0 < |x - a| < δ
0 < |x - 4| < δ

|x - 4| < δ

δ = ε/2

|x - 4| < δ
|x - 4| < ε/2
2 . |x - 4| < ε
|2x - 8| < ε
|2x + 1 - 9| < ε
|f(x) - L| < ε
​

Answer 1

Lim (2x + 1) = 9

x → 4

| f(x) - L | < ε

| 2x + 1 - 9 | < ε

| 2x - 8 | < ε

| 2 . (x - 4) | < ε

2 . |x - 4 | < ε

|x - 4| < ε/2

0 < |x - a| < δ

0 < |x - 4| < δ

|x - 4| < δ

δ = ε/2

|x - 4| < δ

|x - 4| < ε/2

2 . |x - 4| < ε

|2x - 8| < ε

|2x + 1 - 9| < ε

|f(x) - L| < ε

Está corretíssimo.