In the following exercises, assume that limx →6 f(x)=4, limx →6 g(x)=9, and limx →6 h(x)=6 . U

step 1 In this problem, we want to find a limit of f of x plus one -third times G of X as X approaches

In the following exercises, assume that limx →6 f(x)=4, limx...

In the following exercises, assume that $\lim _{x \rightarrow 6} f(x)=4, \lim _{x \rightarrow 6} g(x)=9, \quad$ and $\lim _{x \rightarrow 6} h(x)=6 .$ Use these three facts and the limit laws to evaluate each limit.
$$\lim _{x \rightarrow 6}\left(f(x)+\frac{1}{3} g(x)\right)$$

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Key Concepts

Sum Law

The sum law for limits asserts that the limit of the sum of two functions is equal to the sum of the limits of those functions, provided both limits exist. This property lets you calculate each limit separately and then add the results together, simplifying the evaluation of limits for composite expressions.

Limit Laws

Limit laws are a set of rules that allow one to evaluate the limit of a function by breaking down complex expressions into simpler parts. They provide properties such as the limit of a sum being the sum of the limits and the limit of a constant times a function being equal to the constant times the limit of the function, assuming that all the individual limits exist.

Constant Multiple Law

The constant multiple law states that if you have a constant multiplied by a function, the limit as the variable approaches a certain value can be calculated by taking the constant out and multiplying it by the limit of the function. This simplifies calculations by allowing the constant to be factored out of the limit operation.

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