SOLUTION: Evaluate the limit. (If an answer does not exist, enter DNE.) lim (9x/tan(x)) x→π/2

Algebra ->  Test -> SOLUTION: Evaluate the limit. (If an answer does not exist, enter DNE.) lim (9x/tan(x)) x→π/2       Log On


   

Question 1093786: Evaluate the limit. (If an answer does not exist, enter DNE.)

lim (9x/tan(x))
x→π/2

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
find:
lim%28x-%3Epi%2F2%2C%289x%29%2Ftan%28x%29%29
Apply the constant multiple rule:
lim%28x-%3Epi%2F2%2Ccf%28x%29%29=c%2Alim%28x-%3Epi%2F2%2Cf%28x%29%29 with c=9 and f%28x%29=x%2Ftan%28x%29
lim%28x-%3Epi%2F2%2C%289x%29%2Ftan%28x%29%29=9%2Alim%28x-%3Epi%2F2%2Cx%2Ftan%28x%29%29

The limit of a quotient is the quotient of limits:


Substitute the variable with value:



Therefore,
lim%28x-%3Epi%2F2%2C%289x%29%2Ftan%28x%29%29=0