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How do you determine the values for which a rational expression is undefined?
A rational expression is not defined whenever the denominator of the expression equals zero. These will be the roots or zeros of the denominator.
Is a rational expression undefined whenever its number is zero?
No. 0/3 is well defined.
What is five fifths in simplest form?
5/5 is 1. Whenever the numerator and denominator is the exact same number, it is equal to 1.
What is the derivative of sin x power 0?
I think you are asking "what is the derivative of [sin(x)]^0=sin^0(x)?" and I shall answer this accordingly. Recall that x^0 = 1 whenever x is not 0. On the other hand, also notice that 0^0 is generally left undefined. Thus, sin^0(x) is the function f(x) such that f(x) is undefined when x = n(pi) and 1 everywhere else. As a result, on every open interval not containing a multiple of pi, i.e. on (n(pi), (n+1)(pi)) the derivative will be zero, since f is just a constant function on these intervals, and whenever x is a multiple of pi, the derivative at x will be undefined. Thus, [d/dx]sin^0(x) is undefined whenever x = n(pi) and 0 everywhere else. In some cases, mathematicians define 0^0 to be 1, and if we were to use this convention, sin^0(x) = 1 for all x, and its derivative would just be 0.
How do you factor x squared minus 4?
x2 - 4 is a special expression that is referred to as a difference of squares. Whenever an expression is in the format: a2 - b2 it can be factored out as: (a + b)(a - b) In the case of x2 + 4, that would be: (x + 2)(x - 2)
