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avatar+1342 

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)→   (          )

 Aug 30, 2019
edited by jjennylove  Aug 30, 2019
 #1
avatar+104683 
+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

 

 

cool cool cool

 Aug 30, 2019
edited by CPhill  Aug 30, 2019
 #2
avatar+104683 
+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  ???

 

 

cool cool cool

 Aug 30, 2019
 #3
avatar+1342 
+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
avatar+104683 
+2

Correct!!!....good job  !!!

 

 

cool cool cool

CPhill  Aug 30, 2019
 #6
avatar+1342 
+1

Awesome! I feel more confident with problmes like this.smiley

jjennylove  Aug 30, 2019

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