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2.2, #4. Given Problem. |
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Part (a).
From both sides, as x approaches 0, the value of f(x) approaches 3. |
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Part (b).
As x approaches 3 from the left side (left-hand limit), the value of the function approaches 4. |
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Part (c).
Simply observe that the ordered pair which has an x-coordinate of 3 is (3,3). |
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Part (d).
The limit doesn't exist, because the left-hand limit as x approaches 3 does not agree with the right-hand limit as x approaches 3. |
Evaluate the function at the given numbers (correct to six decimal
places). Use the results to guess the value of the limit, or explain why
it does not exist.
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2.2, #12. Given Problem. |
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Use a calculator or spreadsheet to calculate each of the y-coordinates for the six given points. |
 
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This guess is made strictly by observing the ordered pairs. |
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2.2, #22. Given Problem. |
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First we look at the numerical evidence. It appears from this data that the limit as x approaches 1 is 6. This appears to be true from both sides of 1. |
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Using Maple, we get the graph at the left
> plot((x^3-1)/(x^(1/2)-1),x=0..1.5); Note that the limit appears to be two-sided and
again appears to be equal to 6. |
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