Pregunta
Ask by Harris Deleon. in Tajikistan
Jan 24,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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Предел функции
при
равен
.
Solución

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Respondido por UpStudy AI y revisado por un tutor profesional
Como
Mind Expander
To analyze the function
as
approaches -1, we can start by factoring both the numerator and the denominator. The numerator
factors to
and the denominator
factors to
.
When substituting
, both the numerator and denominator equal zero, indicating a potential indeterminate form. We can simplify the function by canceling the common factor
, leading to
for
. Now, we can easily evaluate the limit as
approaches -1:
So, the limit is
.
Simplifying expressions is a powerful technique in calculus! A common mistake is forgetting to factor correctly, leading to improper interpretations of limits, especially when facing indeterminate forms. Always double-check if you can simplify before substituting directly, as this can save time and prevent errors!

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