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

Enter your answer by filling in parentheses

As x→−∞ , f(x)→ ( )

As x→∞ , f(x)→ ( )

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 !!!!

CPhill 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

CPhill Aug 28, 2019