Which properties of limits are applicable to find the limit of a rational function at a...

Which properties of limits are applicable to find the limit of a rational function at a particular point?

Expert Solution

The degree of the quotient functions determines the characteristics of the behavior of limits of given rational functions.

The limit of a rational function is determined in the following way:
Recognize the Rational Function:
Firstly, it is required to recognize whether a function is rational function. It must be is the form of f(x)/g(x), where f(x) and g(x) are polynomials and g(x) is not equal to zero.

Direct Substitution:
Find the value of function at given point by directly substituting the value in place of input variable in the function. If we get any one of the indeterminate forms (0 x ?, ? x ?, ?/?, 0/0, ? - ?, 0⁰, ?⁰ and 1^?), then we should jump to the next step. Otherwise, we get our answer

Factorization:
Now, factorize the numerator and denominator of the given function as much as possible and rewrite the function after cancelling out all the common factors

Apply Limits:
Now, substitute the given limits in the function so obtained and obtain the required answer.

jeff jeffy answered 2 years ago

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