Limits

Answer all the questions below and press submit to see how many you got right.

id: 17112

$\lim \limits_{x\to\infty} f(x)=13$ means which of the following?

  • For every $\epsilon>0$ there is a $x$, so that $\lvert f(x)-f(13) \rvert<\epsilon.$
    For every $\epsilon>0$ there is a $y$, so that $\lvert f(x)-13 \rvert<\epsilon$ for all $x<y.$
    For every $\epsilon>0$ there is a $x$, so that $\lvert f(x)-13 \rvert<\epsilon.$
    For every $\epsilon>0$ there is a $y$, so that $\lvert f(x)-13 \rvert<\epsilon$ for all $x>y.$
id: 17085

$\lim \limits_{x\to\infty} \frac{6}{x}=?$

id: 17136

$\lim \limits_{x\to-2} f(x)=3$ means which of the following?

  • For every $\epsilon>0$ there is a $\delta>0$ and a $x$ with $\lvert x--2 \rvert<\delta$ and $\lvert f(x)-3 \rvert<\epsilon.$
    There is an $\epsilon>0$ and a $\delta>0$, so that $\lvert f(x)-3 \rvert<\epsilon$ for all $x$ with $\lvert x--2 \rvert<\delta.$
    For every $\epsilon>0$ there is a $\delta>0$, so that $\lvert f(x)-3 \rvert<\epsilon$ for all $x$ with $\lvert x--2\rvert<\delta.$
    There is an $\epsilon>0$, a $\delta>0$ and a $x$ with $\lvert x--2 \rvert<\delta$ and $\lvert f(x)-3 \rvert<\epsilon.$