How do you solve #x^3-2x>1#?
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To solve the inequality (x^3 - 2x > 1), we first set the inequality equal to zero to find the critical points:
(x^3 - 2x - 1 > 0).
Next, we find the roots of the equation:
(x^3 - 2x - 1 = 0).
Using numerical methods or a graphing calculator, we find that the roots are approximately -1.32, 0.62, and 1.70.
These roots divide the number line into four intervals: ((-∞, -1.32)), ((-1.32, 0.62)), ((0.62, 1.70)), and ((1.70, ∞)).
We then test a value in each interval in the inequality (x^3 - 2x > 1) to determine the sign of the expression in each interval.
For example, for (x = -2), ( (-2)^3 - 2(-2) > 1), which is true. Therefore, the interval ((-∞, -1.32)) is part of the solution.
For (x = 0), (0^3 - 2(0) > 1), which is false. Therefore, the interval ((-1.32, 0.62)) is not part of the solution.
For (x = 1), (1^3 - 2(1) > 1), which is false. Therefore, the interval ((0.62, 1.70)) is not part of the solution.
For (x = 2), (2^3 - 2(2) > 1), which is true. Therefore, the interval ((1.70, ∞)) is part of the solution.
Thus, the solution to the inequality (x^3 - 2x > 1) is ((-∞, -1.32) ∪ (1.70, ∞)).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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