Limit of a polynomial function f(x)
The limit of a polynomial function f(x) as x approaches a particular value, let’s say c, tells us the behavior of the function near that point
The limit of a polynomial function f(x) as x approaches a particular value, let’s say c, tells us the behavior of the function near that point. In other words, it lets us know what value f(x) gets closer to as x gets arbitrarily close to c.
To find the limit of a polynomial function, you can evaluate the function at the specific value c, and that will give you the value that f(x) approaches. However, there is also a general rule that applies to polynomial functions.
For a polynomial function f(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + … + a₁x + a₀, where aₙ, aₙ₋₁, …, a₀ are constants and xⁿ represents the highest degree of the polynomial:
1. If n is even, then as x approaches c, f(x) approaches aₙcⁿ. This means that the value of the function gets closer and closer to a constant value as x gets closer to c.
2. If n is odd, then as x approaches c, f(x) either approaches positive infinity (+∞) or negative infinity (-∞) depending on the sign of aₙ. If aₙ > 0, f(x) approaches +∞, and if aₙ < 0, f(x) approaches -∞. It's important to note that these rules apply when x approaches a value within the domain of the polynomial function. If x approaches a value outside the domain, then the limit may not exist. Let me know if you need further clarification or if you have any additional questions.
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