Given the function f (x) = SiNx, x < and = 0, X is not equal to 0, x > 0, then f (0) =?

Given the function f (x) = SiNx, x < and = 0, X is not equal to 0, x > 0, then f (0) =?

sin0=0

Corollary: if the derivative of a function in interval I is always 0, then it is a constant in interval. Why is it a constant and can't be piecewise?
For example, y = 2, x = 1
That's two constants, right?

If the derivative on the interval I is always 0, then it is a constant on the interval
Notice that it's a constant in the interval
Follow your example
If the derivative is not zero at x = 1, then it is not constant here
If the derivative is 0 in the interval (- infinity, 1), then it is a constant in this interval (- infinity, 1)

How to prove that a function whose derivative is constant is a linear function

Let the derivative f 'of function f be equal to the constant C. consider the function g (x) = f (x) - CX, then G' is equal to 0. By using the Lagrange mean value theorem in differential calculus, for any domain of definition x, y, if X