?Suppose that $\lim _{x \rightarrow a} f(x)=\infty$ and \(\lim _{x \rightarrow a}

Chapter 2, Problem 44

(choose chapter or problem)

Suppose that $\lim _{x \rightarrow a} f(x)=\infty$ and $\lim _{x \rightarrow a} g(x)=c$, where $c$ is a real number. Prove each statement.

(a) $\lim _{x \rightarrow a}[f(x)+g(x)]=\infty$

(b) $\lim _{x \rightarrow a}[f(x) g(x)]=\infty \quad$ if $c>0$

Equation Transcription:

${lim}_{x\rightarrow{}a}f(x)=\infty{}$

${lim}_{x\rightarrow{}a}g(x)=c$

$\lim\limits_{{x} \rightarrow {a}}[f(x)+g(x)]=\infty{}$

$\lim\limits_{{x} \rightarrow {a}}[f(x)g(x)]=\infty{}$

$c>0$

$\lim\limits_{{x} \rightarrow {a}}[f(x)g(x)]=-\infty{}$

Text Transcription:

lim_x right arrow a f(x)=infinity

lim_x right arrow a g(x)=c

lim_x right arrow a a [f(x)+g(x)]=infinity

lim_x right arrow a a[f(x)g(x)]=infinity

c>0

lim_x right arrow a [f(x)g(x)]= -infinity

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?Suppose that \(\lim _{x \rightarrow a} f(x)=\infty\) and \(\lim _{x \rightarrow a}