quite rusty...
Would anyone help with the following, please:
lim_{c_pi/2}[(X+tanC)/(1-XtanC)] =?
I don't understand why, in a book, they continue thus:
lim_{c_pi/2}[sec^{2}C/(-Xsec^{2}C] = -1/X
Thank you in advance
.
Your book is using L'Hôpital's rule, which essentially states that if given:
$\displaystyle L=\lim_{u\to c}\frac{f(u)}{g(u)}$
and:
$\displaystyle \lim_{u\to c}f(u)=\lim_{u\to c}g(u)=0$ or $\displaystyle \lim_{u\to c}f(u)=\lim_{u\to c}g(u)=\infty$
then:
$\displaystyle L=\lim_{u\to c}\frac{f'(u)}{g'(u)}$
Do you see that if you write the limit you are given as:
$\displaystyle -\lim_{c\to\frac{\pi}{2}}\frac{x+\tan(x)}{x\tan(c)-1}$
you have the second indeterminate form above $\displaystyle \frac{\infty}{\infty}$?