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if $\lim_{x \to c} f(x)$ is exists and $\lim_{x \to c} g(x)$ does not exists,...
if $\lim_{x \to c} f(x)$ is exists and $\lim_{x \to c} g(x)$ does not exists, then $\lim_{x \to c} (f(x) + g(x))$ doesn't existsProof;If we show that if $\lim_{x \to c} f(x)$ and $\lim_{x \to c} (f(x)...
View ArticleAnswer by Fred for if $\lim_{x \to c} f(x)$ is exists and $\lim_{x \to c}...
Your proof is correct. A shorter proof reads as follows:Assumme that $\lim_{x \to c} f(x)$ and $\lim_{x \to c} (f(x) + g(x))$ exists.Since $g=f+g-f$ it follws that $\lim_{x \to c} g(x)$ exists.
View ArticleAnswer by Siminore for if $\lim_{x \to c} f(x)$ is exists and $\lim_{x \to c}...
You do not use quantifiers properly. In particular, to prove that a function has a limit, you must pick any $\epsilon>0$ and prove the existence of some $\delta>0$ such that etc. Anyway, your...
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