True
A rational expression is not defined whenever the denominator of the expression equals zero. These will be the roots or zeros of the denominator.
No. 0/3 is well defined.
5/5 is 1. Whenever the numerator and denominator is the exact same number, it is equal to 1.
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.
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)
A rational expression is not defined whenever the denominator of the expression equals zero. These will be the roots or zeros of the denominator.
False
Yes, it is true.
A rational number is any number that can be expressed as a fraction. It becomes meaningless or undefined when the lower number, the denominator, its 0 (zero)
false
No. 0/3 is well defined.
Whenever we are dealing with rational fractions.
To solve rational expressions, first, factor both the numerator and the denominator whenever possible. Next, identify any common factors that can be canceled out to simplify the expression. If the expression includes an equation, set the simplified form equal to zero to find the variable's value, and ensure to check for any excluded values that make the denominator zero. Finally, express the solution in its simplest form.
Whenever you solve a rational equation you must make sure the result obtained for an answer does not allow the denominator of one of the rational expressions to assume a value of ZERO, as division by zero is undefined and therefore prohibited. For example if we have 2x/(x-3) =(x2 -9x)/ x when we multiply out by x(x-3) we get 2x(x) = (x2 -9x)(x-3) so 2x2 = x(x-9)(x-3) 2x2 = x(x2 - 12x + 27) 2x2 = x3 - 12x2 + 27x so 0 = x3 - 14x2 + 27x 0 = x(x2 - 14x + 27) so solutions are 0 and 7 + √22 and 7 -√22 but 0 makes right hand side expression have zero in denominator so it is not a solution. We actually have to look at all obtained solutions to be sure they ae not extraneous. Suppose we had obtained a 3 for a solution. That would make the left side denominator equal zero and we would have to dismiss that, if 3 was obtained. The two irrational solutions we have obtained are genuine solutions as neither introduces a zero to a denominator
Yes it does: whenever you find an equivalent fraction.
cause whenever he sees little boys he makes that facial expression
-Pi is irrational, because it does not terminate or repeat. Whenever you multiply an irrational number by a rational number (-1), the result is an irrational number.