Question 1093786
find:
 {{{lim(x->pi/2,(9x)/tan(x))}}}

Apply the constant multiple rule:

{{{lim(x->pi/2,cf(x))=c*lim(x->pi/2,f(x))}}} with {{{c=9}}} and {{{f(x)=x/tan(x)}}}

{{{lim(x->pi/2,(9x)/tan(x))=9*lim(x->pi/2,x/tan(x))}}}


The limit of a quotient is the quotient of limits:

{{{lim(x->pi/2,(9x)/tan(x))=(9*lim(x->pi/2,x))/(lim(x->pi/2,tan(x)))}}}


Substitute the variable with value:


{{{lim(x->pi/2,(9x)/tan(x))=(9*pi)/(2lim(x->pi/2,tan(x)))=0}}}


Therefore,

{{{lim(x->pi/2,(9x)/tan(x))=0}}}