Math Problem Statement
Soit f la fonction définie sur ℝ par : f(x) = 7e^{-x^4}. Le but de cet exercice est de calculer par étapes la limite de f en +∞. 1. La fonction f est de la forme ke^u avec : u(x) = ? et k = ?
Solution
The problem asks us to analyze the function , write it in the form , and later compute the limit of as .
1. Expressing in the form :
We can rewrite as: where:
- ,
- .
Thus:
Let me know if you'd like a step-by-step breakdown or have additional questions.
Related Questions to Expand Understanding
- What happens to as ?
- Why does the exponential term approach 0 as ?
- How would you compute for the same function?
- Can you find the derivative to determine how the function behaves?
- What is the effect of the constant on the overall shape of the function?
Quick Tip
When analyzing limits involving exponential functions, focus on the exponent's growth or decay rate, as this often determines whether the exponential term approaches , , or remains finite.
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Math Problem Analysis
Mathematical Concepts
Exponential Functions
Limits
Asymptotic Behavior
Formulas
f(x) = ke^{u(x)}
Theorems
Exponential Growth and Decay Behavior
Suitable Grade Level
Grades 10-12