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What is the difference between undefined slope and zero slope?
A line with an undefined slope is a vertical line. A line with a slope of zero is a horizontal line. If you use the formula for slope m = (y2-y1) divided by (x2-x1)... For an undefined slope you will get zero in the denominator, which you cannot have because you cannot divide by zero. For a slope equal to zero, you will get a zero in the numerator. Zero divided by any non-zero denominator, will give you a slope of zero.
When the denominator is zero in a rational function what is that called?
Undefined.
A rational expression is undefined whenever its numerator is zero?
false
Why is zero to the power of zero undefined?
Zero to any power is zero; any non-zero number to the power zero is one. Thus, zero to the power zero is sort of contradictory.
Why is division by zero undefined?
Division by zero is undefined because when the limit of 1/x is taken from the positive side of the graph it approaches infinity but when it approaches from the negative side it is negative infinity; thus, becoming an infinite discontinuity this kind of discontinuity makes it undefined. Hope this helps You learn about limits in Calculus. -Joshua Garrison
