The Sum/Difference Rule for Limits | Simplify Limit Evaluation by Applying the Sum and Difference Rule

Sum/ difference rule for limits

The sum/difference rule for limits states that if you have two functions f(x) and g(x), and both of them have limits as x approaches a, then the limit of their sum or difference as x approaches a is equal to the sum or difference of their respective limits

The sum/difference rule for limits states that if you have two functions f(x) and g(x), and both of them have limits as x approaches a, then the limit of their sum or difference as x approaches a is equal to the sum or difference of their respective limits.

More precisely, if lim[x->a]f(x) = L and lim[x->a]g(x) = M, then you can apply the sum/difference rule to find the limit of the sum or difference of f(x) and g(x) as x approaches a:

1. Sum rule: lim[x->a](f(x) + g(x)) = L + M
2. Difference rule: lim[x->a](f(x) – g(x)) = L – M

This rule allows us to simplify the evaluation of limits by breaking down the function into individual parts and evaluating the limits of those parts separately.

It is important to note that this rule only applies when the limits of f(x) and g(x) exist separately. In other words, both f(x) and g(x) must have finite limits as x approaches a.

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