Estimate the following limit: [ lim _{x ightarrow 6} frac{x^{3}-3 x^{2}-21 x+18}{x-6} ] Answer: (The answer will be an integer or whole number) Submit Question
Added by Harman K.
Close
Step 1
The factored form of the numerator is (x-6)(x^2+3x-3). So, the expression becomes: \[ \lim _{x \rightarrow 6} \frac{(x-6)(x^{2}+3x-3)}{x-6} \] We can cancel out the (x-6) terms in the numerator and denominator, leaving us with: Show more…
Show all steps
Your feedback will help us improve your experience
Sanchit Jain and 60 other Calculus 2 / BC 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
Find the limit. $\lim _{x \rightarrow-3^{-}} \frac{x^{2}+2 x-3}{x^{2}+x-6}$
Limits and Their Properties
Infinite Limits
Find the limits. $$\lim _{x \rightarrow 3} \frac{x^{2}-x-6}{x-3}$$
Limits
Limits at Infinity; Infinite limits
Find the limit (if it exists). $$ \lim _{x \rightarrow-3} \frac{x^{2}+x-6}{x^{2}-9} $$
Evaluating Limits Analytically
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD