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Corollary 4.2.4 (Algebraic Limit Theorem for Functional Limits). Let $f$ and $g$ be functions defined on a domain $A \subset \mathbb{R}$, and assume $\lim_{x \to c} f(x) = L$ and $\lim_{x \to c} g(x) = M$ for some limit point $c$ of $A$. Then, (i) $\lim_{x \to c} kf(x) = kL$ for all $k \in \mathbb{R}$, (ii) $\lim_{x \to c} [f(x) + g(x)] = L + M$, (iii) $\lim_{x \to c} [f(x)g(x)] = LM$, and

          Corollary 4.2.4 (Algebraic Limit Theorem for Functional
Limits).
Let $f$ and $g$ be functions defined on a domain $A \subset \mathbb{R}$, and
assume $\lim_{x \to c} f(x) = L$ and $\lim_{x \to c} g(x) = M$ for some limit point $c$
of $A$. Then,
(i) $\lim_{x \to c} kf(x) = kL$ for all $k \in \mathbb{R}$,
(ii) $\lim_{x \to c} [f(x) + g(x)] = L + M$,
(iii) $\lim_{x \to c} [f(x)g(x)] = LM$, and

Corollary 4.2.4 (Algebraic Limit Theorem for Functional
Limits).
Let f and g be functions defined on a domain A ⊂ℝ, and
assume limx → c f(x) = L and limx → c g(x) = M for some limit point c
of A. Then,
(i) limx → c kf(x) = kL for all k ∈ℝ,
(ii) limx → c [f(x) + g(x)] = L + M,
(iii) limx → c [f(x)g(x)] = LM, and

Added by Sharon W.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

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Solved by Expert Georgiann Andersen

Step 1

2.4 (Algebraic Limit Theorem for Functional Limits). This theorem deals with the limits of functions and how they behave under certain algebraic operations. It assumes that we have two functions, $f$ and $g$, defined on a domain $A \subseteq \mathbb{R}$, and Show more…

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Corollary 4.2.4 (Algebraic Limit Theorem for Functional Limits). Let f and g be functions defined on a domain A âŠ† R, and assume limxâ†’cf(x)=L and limxâ†’cg(x)=M for some limit point c of A. Then, (i) limxâ†’c kf(x)=kL for all k âˆˆ R (ii) limxâ†’c [f(x)+g(x)]=L+M (iii) limxâ†’c [f(x)g(x)]=LM