Question

lim x tends to 3π/4. cot x/(2+ cot x)​

Answer 1

Step-by-step explanation:

\begin{gathered} \lim _{x \to3\pi} \frac{4 \cot(x) }{2 + \cot(x) } \\ \\ = \lim _{x \to3\pi} \frac{4 \frac{1}{ \tan(x) } }{2 + \frac{1}{ \tan(x) } } \\ \\ = \lim _{x \to3\pi} \frac{4 }{2 \tan(x) +1 } \\ \\ as \: \: x \to3\pi \: \: then \: \tan(x) \to0 \\ = 4\end{gathered}

x→3π

lim

2+cot(x)

4cot(x)

=

x→3π

lim

2+

tan(x)

1

4

tan(x)

1

=

x→3π

lim

2tan(x)+1

4

asx→3πthentan(x)→0

=4