Create a table of values for the function and use the result to explain why the limit does not exist.
Given: Function
Consider few values less than 0 and few values greater than 0
Then evaluate function value at these values and notice the pattern
If they approach to a certain value and the value is same from both side, than we say the limit exist and equal to that value otherwise the limit does not exist
x = -0.1, f(-0.1) = 3|-0.1|/(-0.1)2 = 30
x = -0.01, f(-0.01) = 3|-0.01|/(-0.01)2 = 300
x = -0.001, f(-0.001) = 3|-0.001|/(-0.001)2 = 3000
x = -0.0001, f(-0.0001) = 3|-0.0001|/(-0.0001)2 = 30000
x = 0.1, f(0.1) = 3|0.1|/(0.1)2 = 30
x = 0.01, f(0.01) = 3|0.01|/(0.01)2 = 300
x = 0.001, f(0.001) = 3|0.001|/(0.001)2 = 3000
x = 0.0001, f(0.0001) = 3|0.0001|/(0.0001)2 = 30000
Hence, the table of values is given by:
| x | -0.1 | -0.01 | -0.001 | -0.0001 | 0 | 0.0001 | 0.001 | 0.01 | 0.1 |
| f(x) | 30 | 300 | 3000 | 30000 | 30000 | 3000 | 300 | 30 |
From the table, we can see as the value of x approach near 0 from both sides, the function value is getting larger and larger without any bound and hence the limit does not exist
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