+1995 What is the limit of the function?
f(x)=4x^11-3x^8+2x-11
Limit Statment
lim f (x) = ∞ True or False
x→−∞
lim f (x) = -∞ True or False
x→∞
I think its False and true and for the second statement -infinity and postings infinity
2. What is the end behavior of the function?
f(x)=−2x^4+5x^3−2x+12
Enter your answer by filling in parentheses
As x→−∞ , f(x)→ ( )
As x→∞ , f(x)→ ( )
+129852 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
4x^3, https://www.desmos.com/calculator/vvd4oqehol
-4x^2, https://www.desmos.com/calculator/p7b3iqjxpk
-4x^3, https://www.desmos.com/calculator/dyayuiza6y
+129852 2)
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 ???
+1995 i think the first one will be negatitive infinity ad the nxt one negattive infinity as well ?
Am I correct?
As x→−∞ , f(x)→ ( negatitive infinity )
As x→∞ , f(x)→ ( negatitve infinity )
