Describe the long run behavior of $f(x) = 3x^5 - 2x^4 + 5x^3 - 4$ As $x \to -\infty$, $f(x) \to ?$ As $x \to \infty$, $f(x) \to ?$
Added by Eddie S.
Close
Step 1
The leading term is the term with the highest power of $x$. For the given function $f(x) = 3x^5 - 2x^4 + 5x^3 - 4$, the leading term is $3x^5$. Show more…
Show all steps
Your feedback will help us improve your experience
Gregory Higby and 58 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Give $\lim _{x \rightarrow-\infty} f(x)$ and $\lim _{x \rightarrow+\infty} f(x).$ $$f(x)=x^{5}+25 x^{4}-37 x^{3}-200 x^{2}+48 x+10$$
Foundation for Calculus: Functions and Limits
Extending the Idea of a Limit
Find the long run behavior of each function as $x \rightarrow \infty$ and $x \rightarrow-\infty$. $$ 6 x^{5}-2 x^{4}+x^{2}+3 $$
Polynomial and Rational Functions
Power Functions & Polynomial Functions
In Exercises $10-15,$ give $\lim _{x \rightarrow-\infty} f(x)$ and $\lim _{x \rightarrow+\infty} f(x)$. $$f(x)=x^{5}+25 x^{4}-37 x^{3}-200 x^{2}+48 x+10$$
A Library of Functions
Limits
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD