Can someone help me with my Calculus BC class please? I need to estimate the limit by substituting smaller and smaller values of h.
lim[h:0,((3+h)^3-27)/(h)]

Question

Can someone help me with my Calculus BC class please? I need to estimate the limit by substituting smaller and smaller values of h.
lim[h:0,((3+h)^3-27)/(h)]

kinggeorge · Answer

Does it tell you a suggested value of $h$ to start with?

anonymous · Answer

The question just says: Estimate the limits in Problems 11-14 by substituting smaller and smaller values of h. For trigonometric functions, use radians. Give answers to one decimal place.

lim as h approaches 0     (3+h)^3-27 over h

kinggeorge · Answer

Well, I would start with $h=1$, and then $h=.5$, then $.1$, and then $.01$, and then $.001$,... or something like that. Basically just plug those different values of $h$ in, and see what you get. Let me know what integer you seem to be approaching

anonymous · Answer

Well I found the answer to be 27 but I've absolutely no idea how. Ha ha.

kinggeorge · Answer

Let's make a table (accurate to 3 decimal places).$$\begin{array}{|c|c|}
\hline h&\frac{(3+h)^3-27}{h}\
\hline 1 & 37\
\hline .5&31.75\
\hline .1&27.91\
\hline.05&27.453\
\hline.01&27.090\
\hline.005&27.045\
\hline.001&27.009\
\hline
\end{array}$$

kinggeorge · Answer

As you can see, as $h$ is approaching 0, the formula is approaching $27$. So you would guess that the limit is approaching is 27.

anonymous · Answer

You don't have to do any factoring? At all? :O i.e., FOIL? and how exactly did you get this table?

kinggeorge · Answer

You don't have to do any kind of factoring at all. Just plug in values and get numbers. 

As for the table, I calculated the values using wolfram alpha. Unless you're asking how I made the actual table. To get that, just copy/paste this into the equation editor.
```
\begin{array}{|c|c|}
\hline h&\frac{(3+h)^3-27}{h}\
\hline 1 & 37\
\hline .5&31.75\
\hline .1&27.91\
\hline .05&27.453\
\hline .01&27.090\
\hline .005&27.045\
\hline .001&27.009\
\hline
\end{array}
```

kinggeorge · Answer

The table was made with $\LaTeX$, and we even have a group dedicated to practicing it if you want to learn more. http://openstudy.com/study#/groups/LaTeX%20Practicing!%20%3A%29

anonymous · Answer

I think I've got it. Thanks for the help dude :D

kinggeorge · Answer

You're welcome.