I’m a recent high school graduate who has experience in AP Calculus and a range of other honors math classes. I enjoy teaching and learning.
Explain in your own words what is meant by the equation $ \displaystyle \lim_{x\to 2} f(x) = 5 $Is it possible for this statement to be true and yet $ f(2) = 3 $?Explain.
Sketch the graph of the function and use it to determine the values of $ a $ for which $ \displaystyle \lim_{x\to a}f(x) $ exists.$ f(x) = \left\{ \begin{array}{ll} 1 + \sin x & \mbox{if $ x < 0 $}\\ \cos x & \mbox{if $ 0 \le x \le \pi $}\\ \sin x & \mbox{if $ x > \pi $} \end{array} \right.$
Use a table of values to estimate the value of the limit. If you have a graphing device, use it to confirm your result graphically.
$ \displaystyle \lim_{x \to 4}\frac{\ln x - \ln 4}{x-4} $
Sketch the graph of a function $ f $ that is continuous except for the stated discontinuity.
Removable discontinuity at 3, jump discontinuity at 5.
Explain why the function is discontinuous at the given number $ a $. Sketch the graph of the function.
$ f(x) = \frac{1}{x + 2} \hspace{55mm} a = -2 $
$ f(x) = \left\{ \begin{array}{ll} x + 3 & \mbox{if $ x \le -1 $} \hspace{40mm} a = -1\\ 2^x & \mbox{if $ x > -1 $} \end{array} \right.$
Please explain how to avoid procrastination
