Question

find the limit. (if the limit is infinite, enter '[infinity]' or '-[infinity]', as appropriate. if the limit does not otherwise exist, enter dne.) lim x→[infinity] x 3x2 4x − 1

Answer 1

To find the limit of the function as x approaches infinity, we look at the term with the highest power of x, which in this case leads to the limit being infinity.

Step-by-step explanation:

The student is asking to find the limit of a function as x approaches infinity. Specifically, the function given seems to be in the form of a polynomial, but it is not completely clear from the question. In general, when finding the limit of a polynomial f(x) = ax^n + bx^(n-1) + ... + z where a, b, ..., z are coefficients and n is the highest power of x, the limit as x approaches infinity is dominated by the term with the highest power of x. In the case where the highest power is in the numerator and it is greater than that in the denominator, like x^3, the limit will be [infinity] if the leading coefficient is positive, and -[infinity] if it's negative.

If we consider the given expression to be f(x) = x + 3x^2 + 4x - 1, the term with the highest power of x is 3x^2. Thus, as x approaches infinity, the limit of the function will be dominated by 3x^2, which leads to [infinity].