Math Problem Statement
Kerjakan soal berikut menggunakan rumus limit trigonometri
Solution
The problem presented is a limit involving a trigonometric function:
To solve this, we will use the standard limit identity for small angles:
where is a constant. In our case, the numerator is , so , and the denominator is .
Here are the steps:
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Rewrite the limit as:
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Apply the standard limit rule:
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Therefore, the limit becomes:
The solution to the limit is:
Let me know if you need more details or have any questions.
Here are five related questions to expand on this concept:
- What is the limit of as ?
- How would you evaluate ?
- Can you use L'Hôpital's Rule to solve ?
- What is the general form of the small angle approximation for trigonometric functions?
- How does the limit behave for larger angles?
Tip: Always check for simplifications involving trigonometric identities before applying limit theorems.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Limits
Calculus
Formulas
lim(x -> 0) (sin(kx)/kx) = 1
lim(x -> 0) sin(2x) / 3x = (1/3) lim(x -> 0) sin(2x)/2x
Theorems
Trigonometric Limit Theorem
Small Angle Approximation
Suitable Grade Level
Grades 10-12