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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

As x→−∞ ,  f(x)→  (        )

As x→∞ ,  f(x)→   (          )

Aug 30, 2019
edited by 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   Aug 30, 2019
edited by CPhill  Aug 30, 2019
#2
+1

2)

Sign on lead term   =  negative

Power on lead term  =  even

Based on my previous answer, do you you see the correct answers  ???   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
edited by jjennylove  Aug 30, 2019
edited by jjennylove  Aug 30, 2019
#5
+2

Correct!!!....good job  !!!   CPhill  Aug 30, 2019
#6
+1

Awesome! I feel more confident with problmes like this. jjennylove  Aug 30, 2019