Multivariable limit problem with cos/cos

[RJLiberator]

Homework Statement

Lim (x,y) --> (pi, 0) of (cos(x-y))/(cos(x+y))

Homework Equations

The answer is 1

The Attempt at a Solution

My answer is this: The function is continuous at the point in question, so we only need to plug in the values which result to be 1.

My question here: I know this function is discontinuous when cos = pi/2 or 3pi/2. As the denominator would be 0. But because my point of interest IS continuous, this allows me to proceed in the manner that I did. Correct?

 

[Dick]

Homework Statement

Lim (x,y) --> (pi, 0) of (cos(x-y))/(cos(x+y))

Homework Equations

The answer is 1

The Attempt at a Solution

My answer is this: The function is continuous at the point in question, so we only need to plug in the values which result to be 1.

My question here: I know this function is discontinuous when cos = pi/2 or 3pi/2. As the denominator would be 0. But because my point of interest IS continuous, this allows me to proceed in the manner that I did. Correct?

Correct. f/g is continuous if f and g are continuous and g is not 0.

 

[RJLiberator]

Excellent. Thank you for the definition.

 

[Dick]

Excellent. Thank you for the definition.

It's not a definition, it's a theorem. But you are welcome.