What should be noted when using the important limit ?
Conditions
- The variable inside the sine function must match the denominator exactly.
- The matched expression must approach 0.
- Angles are in radians.
Reasoning, step by step
- Identify the argument of the sine function.
- Check if the denominator is exactly the same as the sine argument.
- Verify that this common expression approaches 0.
- Apply the limit value of 1.
Example
The video uses a red box to highlight that in , the inside the sine matches the in the denominator, and both approach 0 as .
Common misconceptions
- Believing that as long as the numerator is sin(some expression) and the denominator is another expression, one can directly apply the conclusion that the limit is 1.
- Forgetting that the limit does not hold if angles are in degrees.
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