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Limits of Rational Functions – Fractions and Square Roots
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What are the limits of a rational function?
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For the limits of rational functions, we look at the degrees of their quotient functions, whether the degree of the numerator function is less than, equal to, or greater than the degree of the denominator function. These characteristics will determine the behavior of the limits of rational functions.
What is limit rational function?
Definition of the Limit of Rational Functions
For the rational function f ( x ) = p ( x ) q ( x ) and any real number , lim x → a f ( x ) = p ( a ) q ( a ) if q ( a ) ≠ 0. If q ( a ) = 0 , then the function may or may not have a limit.
Does the limit of rational functions always exist?
Not necessarily. Remember, in determining a limit of a function as x approaches a, what matters is whether the output approaches a real number as we get close to x=a. The existence of a limit does not depend on what happens when x equals a. limx→7f(x)=limx→7g(x).
Which rule may be used in finding limits of rational functions?
Rational functions, like (x^2-4)/(x-2), are continuous on their domain, so the substitution rule applies when evaluating limits of rational functions within their domains.
Does the limit of rational functions always exist?
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Not necessarily. Remember, in determining a limit of a function as x approaches a, what matters is whether the output approaches a real number as we get close to x=a. The existence of a limit does not depend on what happens when x equals a. limx→7f(x)=limx→7g(x).
Does the limit of a rational function exist?
If the degree of the numerator is equal to the degree of the denominator, then the limit of the rational function is the ratio of the leading coefficients. 3. If the degree of the numerator is greater than the degree of the denominator, then the limit of the rational function does not exist.
Why would a limit not exist?
In short, the limit does not exist if there is a lack of continuity in the neighbourhood about the value of interest. Recall that there doesn’t need to be continuity at the value of interest, just the neighbourhood is required.
Does the limit of a polynomial function always exist?
Not necessarily. Remember, in determining a limit of a function as x approaches a, what matters is whether the output approaches a real number as we get close to x=a. The existence of a limit does not depend on what happens when x equals a. limx→7f(x)=limx→7g(x).
References:
Limits of rational functions – Examples and Explanation
Limits of Rational Functions – Online Math Learning
Limit of a Rational Function – Free math help – mathportal.org
Limits of Rational Functions – Concept – Brightstorm
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