[SPLIT] lim{x -> 0} { (sec[x] - 1) / (x sec[x]) }

[Cambelljose]

actually i could use help on this last one.

lim sec(x)-1
_{x -> 0 (x)sec(x)}

 

[stapel]

actually i could use help on this last one.

lim sec(x)-1
_{x -> 0 (x)sec(x)}

What have you tried? (Hint: What was suggested in your other thread involving a limit?)

After you converted to cosines and simplified, did you notice that the limit looked vaguely familiar? (Hint: Look back in your book to the section where they "proved" some trig limits or derivatives. They did a long discussion of a limit with cosine (and another one with sine), and you probably wondered why they carried on about it. This exercise here is why.)

 

[Cambelljose]

Thnx again, I was aple to simply it to that equation but I kept wondering why it equaled 0. My teacher taught it to us and he told us to remember it, I guess I should follow his advice from now on. Thank you for all of your help.

 

[HallsofIvy]

I presume that, after rewriting "sec(x)" as "1/cos(x)" and multiplying both numerator and denominator by "cos(x)" you got to $\displaystyle \frac{1- cos(x)}{x}$. The limit $\displaystyle \lim_{x\to 0} \frac{1- cos(x)}{x}= 0$, along with $\displaystyle \lim_{x\to 0}\frac{sin(x)}{x}= 1$, are very important and very fundamental limits. How you get them depends on exactly how you have defined "cos(x)" and "sin(x)".