Math Problem Statement
(sin3x)/x
Solution
The expression is undefined at because division by zero is not allowed. However, we can explore the behavior of this function for small values of , particularly as approaches 0, which can be useful in calculus.
Finding the Limit as Approaches 0:
To evaluate this limit, we can use the standard limit result:
In this case, , so:
Thus, the limit of as approaches 0 is 3.
Would you like to explore further details, or do you have any questions?
Here are 5 related questions:
- How would you compute for different values of ?
- What is the derivative of ?
- How does the graph of behave as increases?
- Can you expand using a Taylor series around ?
- What happens to for large values of ?
Tip: Knowing common limits like can help in evaluating more complex limits efficiently.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Limits
Calculus
Formulas
lim_{x → 0} (sin(kx)/x) = k
Theorems
Sine Limit Theorem
Suitable Grade Level
Grades 11-12