at what point is the function y=cos/(5x) continuous?
It is continuous anywhere the denominator is not zero.
Should that be y=cos(x)/(5x)?
That is for every real number except x=0
To determine at what point the function y = cos(5x) is continuous, we need to consider the conditions for continuity.
A function is continuous if it satisfies three conditions:
1. The function is defined at the point in question.
2. The limit of the function exists at that point.
3. The value of the function at that point equals the limit.
In the case of the function y = cos(5x), the cosine function is continuous everywhere. Therefore, the function y = cos(5x) is defined and continuous for all values of x. There are no specific points where the function is discontinuous.
To determine at which point the function y = cos(5x) is continuous, we need to consider the nature of the function and any potential points of discontinuity.
First, let's note that the function y = cos(5x) consists of the cosine function, which is known to be continuous for all real numbers. Therefore, the only possible points of discontinuity would come from the denominator, 5x.
For the function to be continuous, there should be no values of x that result in division by zero (since division by zero is undefined in mathematics). Hence, we need to find the values of x for which 5x = 0.
Solving the equation 5x = 0, we find x = 0. Thus, x = 0 is the only point at which the function y = cos(5x) may be discontinuous due to division by zero.
However, since the cosine function is defined for all real numbers, the entire function y = cos(5x) is continuous for all values of x except x = 0.