Question

How to find the limit of a function.

Answer 1

To find the limit of a function, you need to evaluate the behavior of the function as the independent variable approaches a specific value or as it approaches infinity or negative infinity. There are several methods to find limits, including direct substitution, factoring, rationalizing, and using special limits.

Step-by-step explanation:

To find the limit of a function, you need to evaluate the behavior of the function as the independent variable approaches a specific value or as it approaches infinity or negative infinity. There are several methods to find limits, including direct substitution, factoring, rationalizing, and using special limits.

For example, if you have the function f(x) = (3x^2 + 2x + 1)/(x + 1), you can find the limit of f(x) as x approaches 2 by substituting the value of x into the function. The result would be (3(2)^2 + 2(2) + 1)/(2 + 1) = 15/3 = 5.

Another method is to use the limit laws, which state that the limit of a sum, difference, product, or quotient of functions is equal to the sum, difference, product, or quotient of their limits. This method can be useful when dealing with functions that cannot be evaluated directly.

Answer 2

In mathematics, the limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular input. Formal definitions, first devised in the early 19th century, are given below. Informally, a function f assigns an output f(x) to every input x.

Step-by-step explanation: