Question

Find the limit. $$ \lim _{x \rightarrow 0^{-}}\left(x^{2}-\frac{1}{x}\right) $$

   Find the limit.
$$
\lim _{x \rightarrow 0^{-}}\left(x^{2}-\frac{1}{x}\right)
$$

Calculus an Applied Approach

Calculus an Applied Approach

Ron Larson, David C,… 8th Edition

Chapter 3, Problem 20

Instant Answer

Solved by Expert Dwijendra Rao

06/13/2021

Step 1

Step 1: We are given the limit as x approaches 0 from the left of the function $x^{2}-\frac{1}{x}$. Show more…

Show all steps

lock

Thanks for your feedback!

Find the limit. $$ \lim _{x \rightarrow 0^{-}}\left(x^{2}-\frac{1}{x}\right) $$

Play audio

Feedback

Powered by NumerAI

Dwijendra Rao and 80 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

One-Sided Limits

One-sided limits analyze the behavior of a function as the variable approaches a particular value exclusively from one direction, either from the left or the right. This concept is crucial when the function exhibits different behavior on either side of the point of interest.

Dominance of Terms

When evaluating limits of functions composed of multiple terms, it is important to determine which term has the most significant impact on the behavior of the function near the limit point. The term with the dominant growth or decay rate can often dictate the overall limit of the function.

Behavior of Reciprocal Functions Near Zero

Reciprocal functions like 1/x experience rapid changes as x approaches zero, with their behavior being highly dependent on the direction of approach. Approaching zero from the negative side, for example, can lead to the function diverging to negative infinity, which is a critical factor in evaluating such limits.

Recommended Videos

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later