Answer:
L=0
Step-by-step explanation:
[tex]L=\lim\limits_{x \rightarrow \frac{\pi}{2}}3secx-3tanx[/tex]
Replacing the value of x we get ∞ - ∞ which is an indetermined expression
We must transform the limit so it can be shown as a fraction and the L'Hopital's rule can be applied:
[tex]L=\lim\limits_{x \rightarrow \frac{\pi}{2}}\frac{3-3sinx}{cosx}=\frac{0}{0}[/tex]
Now we can take the derivative in both parts of the fraction
[tex]L=\lim\limits_{x \rightarrow \frac{\pi}{2}}\frac{-3cosx}{-sinx}=3\lim\limits_{x \rightarrow \frac{\pi}{2}}\frac{cosx}{sinx}=3\times 0=0[/tex]
