Finding Limits at Infinity: x^4 + x^5

In summary, the limit as x approaches minus infinity of x^4 + x^5 is equal to minus infinity since the equation is in the form of infinity minus infinity. However, by factoring the expression, we can see that it is equal to minus infinity since infinity multiplied by negative infinity equals negative infinity.
  • #1
EvilBunny
39
0
lim as x goes closer to minus infinity.


x^4 + x^5


now visibly the answer is minus infinity since the equation are simple. But aside from saying x^5 is bigger then x^4 could there be anything else to do ?
 
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  • #2
EvilBunny said:
lim as x goes closer to minus infinity.


x^4 + x^5


now visibly the answer is minus infinity since the equation are simple. But aside from saying x^5 is bigger then x^4 could there be anything else to do ?

why would the answer be minus infinity?
 
  • #3
well as the expression is written right now
you cannot tell what the limit is since you will end up with infinity-infinity, which is an intermediate form, or how do u call it in english! But hopefully there is sth we can do to avoid this, here:

x^4+x^5=x^4(x+1) so now infinity*(-infinity)=-infinity
 

Related to Finding Limits at Infinity: x^4 + x^5

1. What is the limit of x^4 + x^5 as x approaches infinity?

The limit of x^4 + x^5 as x approaches infinity is infinity. This is because as x gets larger and larger, the value of x^4 and x^5 also increase without bound.

2. How do you find the limit at infinity of a polynomial function?

To find the limit at infinity of a polynomial function, you can use the leading term of the polynomial. In this case, the leading term is x^5. Since the degree of the polynomial is odd, the limit at infinity will be either positive infinity or negative infinity, depending on the sign of the coefficient of the leading term.

3. Can the limit at infinity of a polynomial function be negative?

Yes, the limit at infinity of a polynomial function can be negative. This depends on the sign of the coefficient of the leading term. If the coefficient is negative, the limit at infinity will also be negative.

4. How does the degree of a polynomial affect the limit at infinity?

The degree of a polynomial affects the limit at infinity in the following ways:

  • If the degree is even, the limit at infinity will be positive infinity or negative infinity depending on the sign of the coefficient of the leading term.
  • If the degree is odd, the limit at infinity will be positive infinity or negative infinity depending on the sign of the coefficient of the leading term.
  • If the degree is 0, the limit at infinity will be equal to the constant term of the polynomial.

5. Can the limit at infinity of a function be a finite number?

No, the limit at infinity of a function cannot be a finite number. This is because when x approaches infinity, the value of the function also approaches infinity. A finite number cannot be reached as x approaches infinity.

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