Math Problem Statement
Solution
To solve this limit problem, we need to find:
Step-by-Step Solution
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Evaluate the form: As , we can see that , , and . So, the expression takes the indeterminate form .
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Apply L'Hôpital's Rule: Since the limit is an indeterminate form of type , we can apply L'Hôpital's Rule, which states that: if the limit exists. Here:
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Differentiate the Numerator :
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Differentiate the Denominator :
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Rewrite the Limit: Substitute and back into the limit:
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Evaluate the New Limit: As :
- , so .
- , so .
This gives:
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Math Problem Analysis
Mathematical Concepts
Calculus
Limits
Trigonometric Functions
Indeterminate Forms
Formulas
L'Hôpital's Rule
Trigonometric limit sin(x)/x as x approaches 0
Theorems
L'Hôpital's Rule
Suitable Grade Level
Grades 11-12
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