Practice problem
Let f:R→Rf:\mathbb{R} \to \mathbb{R}f:R→R, fix a∈Ra \in \mathbb{R}a∈R, and assume limx→a+f(x)=∞\lim_{x \to a^+} f(x) = \inftylimx→a+f(x)=∞. Which of the following are true about one-sided limits?
For all positive constants α\alphaα and β\betaβ, limx→a+(α⋅f(x)+β)=∞\lim_{x \to a^+} (\alpha \cdot f(x) + \beta) = \inftylimx→a+(α⋅f(x)+β)=∞.
limx→a−f(x)\lim_{x \to a^-}f(x)limx→a−f(x) is either ∞\infty∞ or −∞-\infty−∞.
For any function ggg, limx→a+(f(x)+g(x))=∞\lim_{x \to a^+}(f(x) + g(x)) = \inftylimx→a+(f(x)+g(x))=∞.
For any function g≠0g \not= 0g=0, limx→a+(f(x)⋅g(x))=∞\lim_{x \to a^+}(f(x) \cdot g(x)) = \inftylimx→a+(f(x)⋅g(x))=∞.
limx→a+−f(x)=−∞\lim_{x \to a^+} -f(x) = -\inftylimx→a+−f(x)=−∞.
For any function ggg, limx→a+g(f(x))=∞\lim_{x \to a^+} g(f(x)) = \inftylimx→a+g(f(x))=∞.
f(a)≠∞f(a) \not= \inftyf(a)=∞.
Type a concept, like “slope” or “photosynthesis”.