A polynomial function is a mathematical function that can be expressed as a sum of terms, each consisting of a constant coefficient multiplied by a variable raised to a non-negative integer power. For example, f(x) = 2x^3 + 5x^2 - 3x + 7 is a polynomial function.
The limits of polynomial functions depend on the degree of the polynomial. A polynomial of degree n will have n+1 possible limits, which can be either positive or negative infinity.
To calculate the limit of a polynomial function, you can use the standard limit rules to simplify the function until you can directly evaluate the limit. Alternatively, you can use the limit definition of a derivative to find the limit at a specific point.
The limits of polynomial functions help us understand the behavior of the function as the input value approaches certain values. They can also help us identify the horizontal asymptotes of the function and determine its end behavior.
No, polynomial functions can only have horizontal asymptotes as limits. They cannot have vertical asymptotes, since polynomials are continuous functions and do not have any breaks or jumps in their graph.