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Question
In problems 1 – 6, using the table estimate the value of the limit
`lim_(x -> 0) sin x/x`
| x | – 0.1 | – 0.01 | – 0.001 | 0.001 | 0.01 | 0.1 |
| f(x) | 0.99833 | 0.99998 | 0.99999 | 0.99999 | 0.99998 | 0.99833 |
Solution
Let f(x) = `sin x/x`
| x | – 0.1 | – 0.01 | – 0.001 | 0.001 | 0.01 | 0.1 |
| f(x) |
`(sin(- 0.1))/(- 0.1)` = `(- sin(0.1))/(- 0.1)` = 0.998 |
`(sin(- 0.01))/(- 0.01)` = `(- sin(0.01))/(- 0.01)` = 0.999 |
`(sin(- 0.001))/(- 0.001)` = `(- sin(0.001))/(- 0.001)` = 0.9999 |
`(sin(0.001))/(0.001)` = 0.9999 |
`(sin(0.01))/(0.01)` = 0.999 |
`(sin(0.1))/(0.1)` = 0.998 |
`lim_(x -> 0) sin x/x` = 1
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