What is the limit of the function?
lim f (x) = ∞ True or False
lim f (x) = -∞ True or False
I think its False and true and for the second statement -infinity and postings infinity
2. What is the end behavior of the function?
Enter your answer by filling in parentheses
As x→−∞ , f(x)→ ( )
As x→∞ , f(x)→ ( )
First one....the first term, 4x^11 will determine the limits in both directions
When x is some large negative, i.e., x approaches negative infinity, 4(-x)^11 = -4x^11 and the function approaches negative infinity
When x is some large positive, i.e., x approaches positive infinity, 4x^11 approaches positive infinity
So...both statements are False
Here's an easy way to remember the end behavior
Sign on Lead Term Power on lead term Behavior at both ends
+ even up [ approaches infinity on both ends]
+ odd down on the left, up on the right
- even down on both sides
- odd up on the left, down on the right
To see this.....look at the following graphs of
4x^2 , https://www.desmos.com/calculator/c9hunr1imw
The lead term is -2x^4
Sign on lead term = negative
Power on lead term = even
Based on my previous answer, do you you see the correct answers ???