Limits and Continuity

Determine all of the values of $x$ where the function $f$ (given below) has discontinuities. At each value where $f$ has a discontinuity, determine if $f$ is continuous from either the right or left at $x$ and also state whether or not the discontinuity is removable.

Determine the value(s) of $k$ that make(s) the function $g$ defined by $\fe{g}{t}=\begin{cases}t^2+kt-k&t\geq3\\t^2-4k&t\lt 3\end{cases}$ continuous over $\ointerval{-\infty}{\infty}$.

Draw sketches of the curves $y=e^x$, $y=e^{-x}$, $y=\fe{\ln}{x}$, and $y=\frac{1}{x}$. Note the coordinates of any and all intercepts. This is something you should be able to do from memory/intuition. If you cannot already do so, spend some time reviewing whatever you need to review so that you can do so. Once you have the graphs drawn, fill in each of the blanks below and decide whether or not each limit exists. The appropriate symbol for…

Draw sketches of the curves $y=e^x$, $y=e^{-x}$, $y=\fe{\ln}{x}$, and $y=\frac{1}{x}$. Note the coordinates of any and all intercepts. This is something you should be able to do from memory/intuition. If you cannot already do so, spend some time reviewing whatever you need to review so that you can do so. Once you have the graphs drawn, fill in each of the blanks below and decide whether or not each limit exists. The appropriate symbol for…

Draw sketches of the curves $y=e^x$, $y=e^{-x}$, $y=\fe{\ln}{x}$, and $y=\frac{1}{x}$. Note the coordinates of any and all intercepts. This is something you should be able to do from memory/intuition. If you cannot already do so, spend some time reviewing whatever you need to review so that you can do so. Once you have the graphs drawn, fill in each of the blanks below and decide whether or not each limit exists. The appropriate symbol for…

Draw sketches of the curves $y=e^x$, $y=e^{-x}$, $y=\fe{\ln}{x}$, and $y=\frac{1}{x}$. Note the coordinates of any and all intercepts. This is something you should be able to do from memory/intuition. If you cannot already do so, spend some time reviewing whatever you need to review so that you can do so. Once you have the graphs drawn, fill in each of the blanks below and decide whether or not each limit exists. The appropriate symbol for…

Draw sketches of the curves $y=e^x$, $y=e^{-x}$, $y=\fe{\ln}{x}$, and $y=\frac{1}{x}$. Note the coordinates of any and all intercepts. This is something you should be able to do from memory/intuition. If you cannot already do so, spend some time reviewing whatever you need to review so that you can do so. Once you have the graphs drawn, fill in each of the blanks below and decide whether or not each limit exists. The appropriate symbol for…

Draw sketches of the curves $y=e^x$, $y=e^{-x}$, $y=\fe{\ln}{x}$, and $y=\frac{1}{x}$. Note the coordinates of any and all intercepts. This is something you should be able to do from memory/intuition. If you cannot already do so, spend some time reviewing whatever you need to review so that you can do so. Once you have the graphs drawn, fill in each of the blanks below and decide whether or not each limit exists. The appropriate symbol for…

Draw sketches of the curves $y=e^x$, $y=e^{-x}$, $y=\fe{\ln}{x}$, and $y=\frac{1}{x}$. Note the coordinates of any and all intercepts. This is something you should be able to do from memory/intuition. If you cannot already do so, spend some time reviewing whatever you need to review so that you can do so. Once you have the graphs drawn, fill in each of the blanks below and decide whether or not each limit exists. The appropriate symbol for…

Draw sketches of the curves $y=e^x$, $y=e^{-x}$, $y=\fe{\ln}{x}$, and $y=\frac{1}{x}$. Note the coordinates of any and all intercepts. This is something you should be able to do from memory/intuition. If you cannot already do so, spend some time reviewing whatever you need to review so that you can do so. Once you have the graphs drawn, fill in each of the blanks below and decide whether or not each limit exists. The appropriate symbol for…

Draw sketches of the curves $y=e^x$, $y=e^{-x}$, $y=\fe{\ln}{x}$, and $y=\frac{1}{x}$. Note the coordinates of any and all intercepts. This is something you should be able to do from memory/intuition. If you cannot already do so, spend some time reviewing whatever you need to review so that you can do so. Once you have the graphs drawn, fill in each of the blanks below and decide whether or not each limit exists. The appropriate symbol for…

Draw sketches of the curves $y=e^x$, $y=e^{-x}$, $y=\fe{\ln}{x}$, and $y=\frac{1}{x}$. Note the coordinates of any and all intercepts. This is something you should be able to do from memory/intuition. If you cannot already do so, spend some time reviewing whatever you need to review so that you can do so. Once you have the graphs drawn, fill in each of the blanks below and decide whether or not each limit exists. The appropriate symbol for…

Draw sketches of the curves $y=e^x$, $y=e^{-x}$, $y=\fe{\ln}{x}$, and $y=\frac{1}{x}$. Note the coordinates of any and all intercepts. This is something you should be able to do from memory/intuition. If you cannot already do so, spend some time reviewing whatever you need to review so that you can do so. Once you have the graphs drawn, fill in each of the blanks below and decide whether or not each limit exists. The appropriate symbol for…

Draw sketches of the curves $y=e^x$, $y=e^{-x}$, $y=\fe{\ln}{x}$, and $y=\frac{1}{x}$. Note the coordinates of any and all intercepts. This is something you should be able to do from memory/intuition. If you cannot already do so, spend some time reviewing whatever you need to review so that you can do so. Once you have the graphs drawn, fill in each of the blanks below and decide whether or not each limit exists. The appropriate symbol for…

Draw sketches of the curves $y=e^x$, $y=e^{-x}$, $y=\fe{\ln}{x}$, and $y=\frac{1}{x}$. Note the coordinates of any and all intercepts. This is something you should be able to do from memory/intuition. If you cannot already do so, spend some time reviewing whatever you need to review so that you can do so. Once you have the graphs drawn, fill in each of the blanks below and decide whether or not each limit exists. The appropriate symbol for…

Draw sketches of the curves $y=e^x$, $y=e^{-x}$, $y=\fe{\ln}{x}$, and $y=\frac{1}{x}$. Note the coordinates of any and all intercepts. This is something you should be able to do from memory/intuition. If you cannot already do so, spend some time reviewing whatever you need to review so that you can do so. Once you have the graphs drawn, fill in each of the blanks below and decide whether or not each limit exists. The appropriate symbol for…

Draw sketches of the curves $y=e^x$, $y=e^{-x}$, $y=\fe{\ln}{x}$, and $y=\frac{1}{x}$. Note the coordinates of any and all intercepts. This is something you should be able to do from memory/intuition. If you cannot already do so, spend some time reviewing whatever you need to review so that you can do so. Once you have the graphs drawn, fill in each of the blanks below and decide whether or not each limit exists. The appropriate symbol for…

Draw sketches of the curves $y=e^x$, $y=e^{-x}$, $y=\fe{\ln}{x}$, and $y=\frac{1}{x}$. Note the coordinates of any and all intercepts. This is something you should be able to do from memory/intuition. If you cannot already do so, spend some time reviewing whatever you need to review so that you can do so. Once you have the graphs drawn, fill in each of the blanks below and decide whether or not each limit exists. The appropriate symbol for…

Draw sketches of the curves $y=e^x$, $y=e^{-x}$, $y=\fe{\ln}{x}$, and $y=\frac{1}{x}$. Note the coordinates of any and all intercepts. This is something you should be able to do from memory/intuition. If you cannot already do so, spend some time reviewing whatever you need to review so that you can do so. Once you have the graphs drawn, fill in each of the blanks below and decide whether or not each limit exists. The appropriate symbol for…