Question:

Let f(x) = 3x^2 - 5x + 2. Find the limit of f(x) as x approaches positive infinity.

Answer:

To find the limit of f(x) as x approaches positive infinity, we need to analyze the behavior of the function as x gets larger and larger.

First, we can determine the leading term of the function. The leading term of a polynomial is the term with the highest power of x, in this case, the term is 3x^2. As x becomes very large, the other terms in the function become insignificant compared to the leading term.

So, as x approaches positive infinity, the function f(x) = 3x^2 - 5x + 2 behaves as 3x^2.

Therefore, the limit of f(x) as x approaches positive infinity is infinity.

Answer:

$\lim_{x \to \infty} (3x^2 - 5x + 2) = \infty$