Limit of sec(x) as x goes to pi/2, does the limit exist?

Thread starter kitle545
Start date Sep 21, 2008
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Limit

In summary, a limit is a fundamental concept in calculus that describes the behavior of a function as its input approaches a certain value. The limit of sec(x) as x approaches pi/2 is undefined, and a limit exists if the left-hand and right-hand limits are equal. Direct substitution cannot be used to evaluate the limit of sec(x) as x approaches pi/2, and this limit is important in understanding the behavior of trigonometric functions.

Sep 21, 2008

kitle545

Homework Statement

lim sec(x)
x-> pi/2 from the left

Homework Equations

The Attempt at a Solution

I wasn't quite sure where to start. I know sec is 1/cos. Does the limit not exist?

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Sep 21, 2008

cse63146

What's the value of cos(pi/2)?

1. What is the definition of a limit?

A limit is a fundamental concept in calculus that describes the behavior of a function as its input approaches a certain value or point. It represents the value that a function approaches as its input gets closer and closer to a specific value, without actually reaching that value.

2. What is the limit of sec(x) as x approaches pi/2?

The limit of sec(x) as x approaches pi/2 is undefined, or does not exist. This is because the secant function is undefined at pi/2, as the cosine of pi/2 is equal to 0, making the secant function approach infinity.

3. How do you determine if a limit exists?

A limit exists if the left-hand limit and the right-hand limit are equal. This means that as x approaches the specific value, the function approaches the same value from both the left and the right side. If the left-hand and right-hand limits are not equal, then the limit does not exist.

4. Can the limit of sec(x) as x approaches pi/2 be evaluated using direct substitution?

No, direct substitution cannot be used to evaluate the limit of sec(x) as x approaches pi/2. This is because direct substitution can only be used when the function is defined at the specific value, but sec(x) is undefined at pi/2.

5. Why is the limit of sec(x) as x approaches pi/2 important?

The limit of sec(x) as x approaches pi/2 is important because it represents the behavior of the secant function near this critical value. It also helps to understand the behavior of other trigonometric functions, such as cosine and tangent, as they are related to the secant function.