How can you tell if an equation has infinitely many solutions?
An equation has infinitely many solutions if every value within the solution set satisfies the equation. This typically occurs when the equation is an identity or if it represents a relationship where one side is a multiple or a factor of the other side. In other words, if the equation simplifies to a true statement regardless of the value chosen for the variables, it has infinitely many solutions.
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Recall that Diophantine equations—equations in which the variable values are restricted to integers or positive integers—may present a very challenging set of numbers to solve.
Euler, for instance, hypothesized that the equation:
contained no non-trivial solutions; however, Noam Elkies discovered one in 1988. As a result, since any solution can be multiplied by a fourth power, there are a limitless number of non-trivial solutions.
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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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