Finding the Limit of (1+x+x^2) as x Approaches 0

Thread starter helpme7
Start date Dec 10, 2008
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SUMMARY

The limit of the expression (1 + x + x^2) as x approaches 0 is definitively 1. This conclusion is derived from evaluating the polynomial at the limit, confirming that the behavior of the function near this point remains stable. Additionally, the expression ((1)^(1/x) - e) simplifies to 1 - e, reinforcing the understanding of limits in calculus.

PREREQUISITES

Understanding of basic calculus concepts, specifically limits.
Familiarity with polynomial functions and their behavior.
Knowledge of exponential functions and the constant e.
Ability to manipulate algebraic expressions involving limits.

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Study the concept of limits in calculus, focusing on polynomial functions.
Explore the properties of the exponential function and its applications.
Learn about L'Hôpital's Rule for evaluating indeterminate forms.
Investigate Taylor series expansions and their relevance to limits.

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Students of calculus, mathematics educators, and anyone interested in understanding the behavior of polynomial limits and exponential functions.

Dec 10, 2008

helpme7

closed.

Last edited: Dec 10, 2008

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Dec 10, 2008

flatmaster

Within a set of parentheses, you will have

1+x+x^2. The limit of this as x--> 0 is 1.

You then have

((1)^(1/x)-e)

One to any power is still one, so

1-e