Simplifying Limits with the Constant Multiple Rule in Mathematics

Constant multiple rule for limits

The constant multiple rule for limits states that if we have a function, say f(x), and we multiply or divide it by a constant, say c, then the limit of c*f(x) as x approaches a will be equal to c times the limit of f(x) as x approaches a

The constant multiple rule for limits states that if we have a function, say f(x), and we multiply or divide it by a constant, say c, then the limit of c*f(x) as x approaches a will be equal to c times the limit of f(x) as x approaches a.

More formally, let’s say we have a function f(x) and another constant c. If lim(x→a) f(x) exists, then lim(x→a) c*f(x) also exists and is equal to c times the value of lim(x→a) f(x).

Mathematically, this can be written as:
lim(x→a) c*f(x) = c * lim(x→a) f(x)

Here, c is any constant, which could be a real number or a constant value. The limit on both sides of the equation needs to exist for this rule to be applicable.

For example, let’s say we have the function f(x) = 2x^2 and we want to find the limit as x approaches 1. According to the constant multiple rule, if we multiply this function by a constant, say 3, the limit will be three times the limit of the original function.

So, lim(x→1) 3*f(x) = 3 * lim(x→1) f(x)
= 3 * lim(x→1) 2x^2
= 3 * 2(1)^2
= 3 * 2
= 6

Therefore, lim(x→1) 3*f(x) = 6.

This rule is helpful in evaluating limits when constants are involved in the function. It allows us to simplify the expression by factoring out the constant and evaluating the limit of the remaining function.

More Answers: