Final answer:
To evaluate the given expression, we find the limit of each term as x approaches negative infinity. After evaluating each term, we combine the limits to determine the overall limit of the expression, which in this case is negative infinity.
Step-by-step explanation:
The given expression is:
Lim (2x + 1)40 (4x - 1)5 (2x + 3)45 as x → -∞
To evaluate this expression, we need to find the limit of each term as x approaches negative infinity.
First, let's consider the term (2x + 1)40:
As x approaches negative infinity, the term 2x becomes more and more negative, and 1 remains constant. So, (2x + 1)40 approaches (-∞)40 = ∞.
Next, let's consider the term (4x - 1)5:
As x approaches negative infinity, the term 4x becomes more and more negative, and -1 remains constant. So, (4x - 1)5 approaches (-∞)5 = -∞.
Finally, let's consider the term (2x + 3)45:
As x approaches negative infinity, the term 2x becomes more and more negative, and 3 remains constant. So, (2x + 3)45 approaches (-∞)45 = ∞.
Now, let's combine the limits of each term:
Lim (2x + 1)40 (4x - 1)5 (2x + 3)45 as x → -∞ = ∞ x -∞ x ∞ = -∞