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(5) (Bonus question): Use the Intermediate Value Theorem to show there is a positive number whose 5th power is exactly 1 more than itself. In other words, there is a positive number which is a solution to the equation x5 = x + 1. Note that you do not need to find x, only show there is such a number.

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  • (5) (Bonus question): Use the Intermediate Value Theorem to show there is a positive number whose 5th power is exactly 1 more than itself. In other words, there is a positive number which is a solution to the equation x5 = x + 1. Note that you do not need to find x, only show there is such a number.


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