Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. When looking for zeros of a rational function, why is the numerator equated to zero and not the denominator?
Ask Question. Asked 6 years, 11 months ago. Active 6 years, 11 months ago. Viewed times. Add a comment. Active Oldest Votes. To see this, consider cases. Taussig N. Taussig Check out this book to see if the club is able to solve the problem. Encourage your kids to be problem solvers!
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Here is another sample page. What is Zero Divided by Zero Equal to? How will this be important in Algebra? Find if it exists. To find the limit of f x when x tends to a there are three different situations that can arise:. W e calculate f a a is put into the expression instead of x. Example 6 Consider the following interval defined function: The graph is shown here.
If this is true for all values of x in the domain of f x then we say that the function is continuous. Conversely if a function is continuous then it is continuous in every point of its domain. This is no problem when considering polynomial functions. Neither do logarithm functions, exponential functions or the square root functions present any problem. When considering we need to look at whether it is the numerator or denominator that increases more rapidly.
However, if the denominator , g x , increases more rapidly then limit is likely to tend to a specific value. When we divide by a number that gets bigger and bigger, the outcome gets smaller and smaller tending to zero. So the limit is zero. Here the denominator increases more rapidly than the numerator, so the fraction gets smaller and smaller tending to zero.
This is the reverse of b. The numerator increases more rapidly and the outcome gets bigger and bigger tending to infinity. We say the limit does not exist. In some texts the limit is said to be infinity. In this example the denominator is of a higher power than the numerator and therefore increases more rapidly. The fraction tends to zero so.
Is 0 if g x increases more rapidly than f x. This happens if, for example, the power of the denominator, g x , is greater than the power of the numerator, f x.
Example 8 Find. What happens when the numerator and denominator are both polynomials of the same degree?
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