Answer :

For a polynomial function p(x), the limit as x approaches a⁻ is determined by the degree of the polynomial and the leading coefficient. It will either be the same as the value of the polynomial at x = a or it will approach -∞ or ∞, depending on the leading coefficient.

To calculate the limit as x approaches a⁻ (from the left) and x approaches a⁺ (from the right) for a polynomial function p(x), we can use the properties of polynomials.

For the limit as x approaches a⁻-:
- When x approaches a⁻ (from the left), we are looking at the values of the polynomial as x gets closer and closer to a from the left side of a.
- If the degree of the polynomial is even, it means that the graph of the polynomial will have a symmetric shape, and as x approaches a⁻ the values of the polynomial will approach the value of the polynomial at x = a.
- If the degree of the polynomial is odd, it means that the graph of the polynomial will have an asymmetric shape, and as x approaches a⁻ the values of the polynomial will either approach -∞ or ∞, depending on the leading coefficient of the polynomial.

In summary, for a polynomial function p(x), the limit as x approaches a⁻ is determined by the degree of the polynomial and the leading coefficient. It will either be the same as the value of the polynomial at x = a or it will approach -∞ or ∞, depending on the leading coefficient.

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