Grade 11 Exam > Grade 11 Videos > Mathematics for Grade 11 > Limits of Trigonometric Functions (includes Sandwich Theorem and Example)
Limits of Trigonometric Functions (includes Sandwich Theorem and Example) Video Lecture | Mathematics for Grade 11
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FAQs on Limits of Trigonometric Functions (includes Sandwich Theorem and Example) Video Lecture - Mathematics for Grade 11
| 1. What are the limits of trigonometric functions? |  |
Ans. The limits of trigonometric functions refer to the values that these functions approach as the input approaches a certain value. For example, the limit of the sine function as the input approaches infinity is 1, and as the input approaches negative infinity, the limit is -1.
| 2. How can the Sandwich Theorem be used to find the limits of trigonometric functions? | |
Ans. The Sandwich Theorem, also known as the Squeeze Theorem, is a powerful tool for finding limits. To use it for trigonometric functions, you can find two simpler functions that "sandwich" the trigonometric function and have the same limit at a certain point. By applying the Sandwich Theorem, you can determine the limit of the trigonometric function.
| 3. Can you provide an example of finding the limit of a trigonometric function using the Sandwich Theorem? | |
Ans. Sure! Let's find the limit of the function f(x) = sin(x)/x as x approaches 0. We can sandwich this function between the bounds g(x) = -1 and h(x) = 1, which are the bounds for the sine function. Since both -1 and 1 have the same limit as x approaches 0, by the Sandwich Theorem, the limit of f(x) must also be the same, which is 0.
| 4. Are there any specific conditions or restrictions when using the Sandwich Theorem for trigonometric functions? | |
Ans. Yes, there are a few conditions to keep in mind when using the Sandwich Theorem. Firstly, the bounds functions used to sandwich the trigonometric function should have the same limit at the desired point. Additionally, the bounds functions should be simple enough to evaluate and compare their limits. Lastly, it's important to ensure that the bounds functions are valid for the entire interval of interest.
| 5. Is the Sandwich Theorem the only method to find the limits of trigonometric functions? | |
Ans. No, the Sandwich Theorem is not the only method to find the limits of trigonometric functions. Other common methods include direct substitution, factoring, rationalizing, and using trigonometric identities. The choice of method depends on the specific function and the limit being evaluated. It's always a good idea to explore different approaches to find the most efficient method for a particular problem.
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Nov 17, 2024 Last updated |
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