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# What is the limit of the function?

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What is the limit of the function?

f(x)=4x^8−3x^7+2x−11

Limit Statment

lim     f (x) = ∞        True or False

x→−∞

lim     f (x) = -∞        True or False

x→∞

I think its True and then False for the second statement

2. What is the end behavior of the function?

f(x)=−2x^5+5x^3−2x+12

As x→−∞ ,  f(x)→  (        )

As x→∞ ,  f(x)→   (          )

Aug 28, 2019
edited by jjennylove  Aug 28, 2019

#1
+2

First one :

The first term  4x^8  will determine the limit at both ends  [ its behavior will "overpower" the other terms ]

Note that when x  = some large positive value   = 4x^8 will be a large positive, i,e, the limit will be + inf

And....when x = some large negative =4x^8 will also be a large positive, i.e., the limit will also be + inf

So...you are correct  !!!!   Aug 28, 2019
#3
+1

Awesome! Thanks jjennylove  Aug 28, 2019
#2
+1

Second one

Again  the highest power term   -2x^5   will determine the end behavior

When  x  is a large negative   -2(-x)^5  =  will be positive

So  as x approaches -inf, f(x)  approaches infinity

On the other hand, when x is a large positive   -2(x)^5  =  will be negative

So  as x approaches inf, f(x) approaches   negative infinity

See the graph here : https://www.desmos.com/calculator/6swdftdxku   Aug 28, 2019
#4
+1

I was unsure whith this one, but it makes sense now. Thank you!

jjennylove  Aug 28, 2019