February 21st, 2017, 01:32 AM  #1 
Member Joined: Feb 2017 From: East U.S. Posts: 40 Thanks: 0  Please teach me how to do this
The limit represents f '(c) for a function f(x) and a number c. Find f(x) and c. lim (Δx>0) [78(1+Δx)]1(1)/Δx So the story is... my teacher assigns this as a homework problem that's gonna turn up on our exam tomorrow, but without going over a single problem with a triangle thing in it. I looked it up and apparently it's a "change" symbol? Please, I really just need the steps written down on how to solve this so I can at least try to learn a little before my next exam in about 11 hours. I'm willing to try to learn, and not just looking for the answer, but I have no time... ANY advice would be great, thanks! 
February 21st, 2017, 02:49 AM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,519 Thanks: 506 Math Focus: Yet to find out. 
The 'little triangle' is an uppercase delta in Greek. And yes, it usually means 'change in'. When you see $\Delta x$, you can say 'change in x'. Although this by itself doesn't mean much. I can't really make out what your function is supposed to be due to some peculiar bracketing. $\displaystyle \lim\limits_{\Delta x \rightarrow 0} \dfrac{7  8(1 + \Delta x)}{\Delta x}$ or, $\displaystyle \lim\limits_{\Delta x \rightarrow 0} 7  8(1 + \Delta x) +\dfrac{1}{\Delta x}$??? Or something else... 
February 21st, 2017, 03:46 AM  #3  
Member Joined: Feb 2017 From: East U.S. Posts: 40 Thanks: 0  Quote:
lim Δx>0 In the numerator of the function, I have "[78(1+Δx)](1)" (there are brackets for some reason) And in the denominator, I just have a "Δx" Hopefully this clarified everything. Last edited by nbg273; February 21st, 2017 at 04:35 AM.  
February 21st, 2017, 04:48 AM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,151 Thanks: 2390 Math Focus: Mainly analysis and algebra 
$$f'(c)= \lim_{\Delta x \to 0} \frac{f(c+\Delta x)  f(c)}{\Delta x}$$ $f(c+\Delta x) = 78(1+\Delta x)$ and $f(c) = 1$. By inspection, you can then suggest a value for $c$ and an expression for $f(x)$. 
February 21st, 2017, 05:03 AM  #5 
Member Joined: Feb 2017 From: East U.S. Posts: 40 Thanks: 0  Sorry, I'm still confused on what f(x) is... I'm bad at math...

February 21st, 2017, 05:29 AM  #6 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,959 Thanks: 801 
It looks like f(x) is intended to be f(x)= 7 8x. Then and . So . That is, for all nonzero , . So what is the limit as goes to 0? 
February 21st, 2017, 06:17 AM  #7 
Member Joined: Feb 2017 From: East U.S. Posts: 40 Thanks: 0  

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