Limit of Trigonometric Function....2

In summary, the limit of a trigonometric function is the value that the function approaches as its input gets closer to a specific value. This can be calculated by substituting the value into the function and simplifying, and the resulting expression may require additional techniques. The limit can also be seen on the graph of the function, and some common trigonometric functions have limits of 1 as the input approaches 0. Understanding the limit of a trigonometric function is important for analyzing and predicting its behavior, as well as determining its continuity and differentiability.
  • #1
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Find the limit of csc(2x) as x tends to pi/2 from the right side.

I decided to graph the function. Based on the graph, I stated the answer to be positive infinity.
According to the textbook, the answer is negative infinity. Why is negative infinity the right answer?

Thanks
 
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  • #2
Problem 1.5.39.
Odd numbered.
Look up the answer and graph it.
 

What is the definition of the limit of a trigonometric function?

The limit of a trigonometric function is the value that a function approaches as the input approaches a certain value or point. It can be calculated using algebraic methods or by graphing the function.

How do you find the limit of a trigonometric function using algebraic methods?

To find the limit of a trigonometric function using algebraic methods, you can use the properties of limits, such as the sum, difference, product, and quotient rules. You can also use trigonometric identities to simplify the function and then apply the limit definition.

What is the relationship between the limit of a trigonometric function and its graph?

The limit of a trigonometric function is the same as the value of the function at that point on its graph. This means that if the function is continuous at that point, the limit and the function value will be the same. However, if the function is not continuous, the limit may not exist.

How do you determine if a limit of a trigonometric function exists?

A limit of a trigonometric function exists if the left-hand and right-hand limits are equal at that point. This means that the function approaches the same value from both sides of the point. If the left-hand and right-hand limits are not equal, the limit does not exist.

What are some common techniques for evaluating limits of trigonometric functions?

Some common techniques for evaluating limits of trigonometric functions include using trigonometric identities, factoring, rationalizing, and applying L'Hopital's rule. It is also helpful to graph the function to visualize the behavior near the limit point.

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