Continuity and limits?

[smileyface497]

I'm having trouble figuring out two similar homework problems involving continuity and limits:

1. Is [e(5+h)-e(5)] / [(5+h)-(5)] continuous at h=0? Why?

2. Calculate the limit as h->0 of [e(5+h)-e(5)] / [(5+h)-(5)].

I have a basic grasp of limits, but this seems waaaay over my head. Please help?

 

[mmm4444bot]

Do you have a definition for some function called e(x) ?

 

[BigGlenntheHeavy]

\(\displaystyle 2. \ \lim_{h\to0}\frac{e^{h+5}-e^5}{(h+5)-5} \ = \ \lim_{h\to0}\frac{(e^h)(e^5)-e^5}{h} \ = \ \lim_{h\to0}\frac{e^5(e^h-1)}{h}\)

\(\displaystyle gives \ the \ indeterminate \ form \ \frac{0}{0}, \ hence \ the \ Marqui's \ time \ to \ go \ to \ work.\)

\(\displaystyle Therefore, \ \lim_{h\to0}\frac{e^5(e^h-1)}{h} \ = \ \lim_{h\to0} (e^5)(e^h) \ = \ e^5.\)

 

[smileyface497]

Oh, I apologize. The "e" shown is not the 2.718 e, but rather it says let e(x) = 125x^2-6.25x^3. (Which simplified is 250x+125h-18.5xh-6.25h^2).

Sorry I left out that bit of information.