In which limits below can we use L'Hopital's Rule?
lim
x
→
0
6
x
cot
x
\displaystyle \lim_{{{x}\rightarrow{0}}}\ \frac{{{6}{x}}}{{\cot{{x}}}}
x
→
0
lim
cot
x
6
x
lim
x
→
0
sin
(
7
x
)
7
x
\displaystyle \lim_{{{x}\rightarrow{0}}}\ \frac{{\sin{{\left({7}{x}\right)}}}}{{{7}{x}}}
x
→
0
lim
7
x
sin
(
7
x
)
lim
x
→
∞
2
x
2
+
3
x
+
6
x
2
+
7
x
−
9
\displaystyle \lim_{{{x}\rightarrow\infty}}\ \frac{{{2}{x}^{{2}}+{3}{x}+{6}}}{{{x}^{{2}}+{7}{x}-{9}}}
x
→
∞
lim
x
2
+
7
x
−
9
2
x
2
+
3
x
+
6
lim
x
→
9
x
−
9
ln
(
10
−
x
)
\displaystyle \lim_{{{x}\rightarrow{9}}}\ \frac{{{x}-{9}}}{{{\ln{{\left({10}-{x}\right)}}}}}
x
→
9
lim
ln
(
10
−
x
)
x
−
9
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