Limit of sin((pi*x*y)/4) at (x,y)--->(-1, 6): 1

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In summary, the limit of sin((pi*x*y)/4) as (x, y)--->(-1, 6) is equal to 1. This is because the value of sin(-3*pi/2) is equal to 1, and as (x, y) approaches (-1, 6), the value of pi*x*y/4 also approaches -3*pi/2, resulting in the same limit.
  • #1
Math10
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Homework Statement


Find the limit of sin((pi*x*y)/4) as (x, y)--->(-1, 6).

Homework Equations


None.

The Attempt at a Solution


I got 1 as the answer. Am I right?
 
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  • #2
Math10 said:

Homework Statement


Find the limit of sin((pi*x*y)/4) as (x, y)--->(-1, 6).

Homework Equations


None.

The Attempt at a Solution


I got 1 as the answer. Am I right?
How did you get 1? Please show your work.
 
  • #3
sin(-3*pi/2)=1, am I right?
 
  • #5
Math10 said:
sin(-3*pi/2)=1, am I right?
Yes, this is correct. My earlier response, which is now deleted, was incorrect. Sorry to have misled you.
 

1. What is the definition of a limit in calculus?

A limit in calculus is the value that a function approaches as the input (x) approaches a certain value.

2. How do you find the limit of a function at a specific point?

To find the limit of a function at a specific point, you can plug in the given point into the function and solve. However, if the function is undefined at that point, you will need to use other methods such as factoring, rationalizing, or using L'Hopital's rule.

3. What is the purpose of finding the limit of a function?

The purpose of finding the limit of a function is to understand the behavior of the function at a specific point. This can help determine if the function is continuous, has a removable/discontinuity, or has infinite or oscillating behavior at that point.

4. How do you solve for the limit of a trigonometric function?

To solve for the limit of a trigonometric function, you can use the properties of trigonometric functions to simplify the function. If the function is still indeterminate, you can use trigonometric identities or the squeeze theorem to evaluate the limit.

5. What is the limit of sin((pi*x*y)/4) at (x,y)--->(-1, 6)?

The limit of sin((pi*x*y)/4) at (x,y)--->(-1, 6) is -1. This can be found by plugging in the given point into the function and solving, or by using the properties of sine and evaluating the limit using the squeeze theorem.

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