Finding the Limit: An Introduction to Calculus

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SUMMARY

The discussion centers on evaluating the limit of the expression lim (x -> ∞) (4x^6 - 6x^5 + 3x^4) / (7x^5 - 6x^4 + 2x^3). It is established that since the degree of the numerator (6) exceeds the degree of the denominator (5), the limit diverges to infinity. This conclusion is reached by rewriting the expression in terms of the highest power of x, which simplifies the evaluation of the limit as x approaches infinity.

PREREQUISITES
  • Understanding polynomial functions and their degrees
  • Familiarity with limits in calculus
  • Basic algebraic manipulation of expressions
  • Knowledge of asymptotic behavior of functions
NEXT STEPS
  • Study the concept of limits in calculus, focusing on polynomial limits
  • Learn about L'Hôpital's Rule for evaluating indeterminate forms
  • Explore the behavior of rational functions as x approaches infinity
  • Practice rewriting expressions to identify dominant terms in limits
USEFUL FOR

This discussion is beneficial for students learning calculus, educators teaching introductory calculus concepts, and anyone seeking to understand polynomial limits and their implications in mathematical analysis.

Gregory.gags
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this may seem like a stupid questions but I'm trying to teach myself basic calculus so I have to start from the very beginning. the question I have is as follows; lim= x -> infinity for 4x^6-6x^5+3x^4 / 7x^5-6x^4+2x^3. (^ mean 'power of') So I read that "because the numerator's degree '6' > the denominators degree '5', the limit diverges". What does that mean, and how does it help me find the limit?
thanks in advance for any help you can give :)
 
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Hi Gregory.gags! :smile:

(try using the X2 button just above the Reply box :wink:)
Gregory.gags said:
this may seem like a stupid questions but I'm trying to teach myself basic calculus so I have to start from the very beginning. the question I have is as follows; lim= x -> infinity for 4x^6-6x^5+3x^4 / 7x^5-6x^4+2x^3. (^ mean 'power of') So I read that "because the numerator's degree '6' > the denominators degree '5', the limit diverges". What does that mean, and how does it help me find the limit?
thanks in advance for any help you can give :)

Rewrite it as x6(4 - 6x-1 + 3x-2)/x5(7 - 6x-1 + 1x-2) :wink:
 

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