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)→ ( )

jjennylove Aug 30, 2019

#1**+2 **

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

CPhill Aug 30, 2019

#2**+1 **

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 ???

CPhill Aug 30, 2019

#3**+1 **

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 )

jjennylove
Aug 30, 2019