Math Problem Statement
Solution
To solve this limit using L'Hospital's Rule, we first need to express it in a form suitable for L'Hospital's Rule. The given limit is of an indeterminate form , so let's proceed with the following steps:
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Transform the Expression:
Consider Take the natural logarithm of both sides to bring the exponent down:
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Apply L'Hospital's Rule:
The form is of type as . Differentiate the numerator and denominator:
Apply L'Hospital's Rule:
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Evaluate the Limit:
As ,
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Exponentiate to Solve for :
Since , then
So, the original limit is:
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Math Problem Analysis
Mathematical Concepts
Limits
Exponential Functions
Logarithms
L'Hospital's Rule
Formulas
L'Hospital's Rule
ln(a^b) = b*ln(a)
lim (x -> 0) ln(1 - 2x)/x
Theorems
L'Hospital's Rule
Suitable Grade Level
Grades 11-12
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