Limits Of Trigonometric Functions

Let

y%3D%5Cdisplaystyle%5Clim%20_%7Bx%20%5Crightarrow%20%5Cinfty%7D%5Cleft(%5Cfrac%7B%5Cpi%7D%7B2%7D-%5Ctan%20%5E%7B-1%7D%20x%5Cright)

Taking log on both sides, we get

%5Cleft(%5Cright.

form

%5Cleft.%5Cfrac%7B%5Cinfty%7D%7B%5Cinfty%7D%5Cright)

%5Clog%20y%3D%5Cdisplaystyle%5Clim%20_%7Bx%20%5Crightarrow%20%5Cinfty%7D%20%5Cfrac%7B1%7D%7Bx%7D%20%5Clog%20%5Cleft(%5Cfrac%7B%5Cpi%7D%7B2%7D-%5Ctan%20%5E%7B-1%7D%20x%5Cright)

%3D%5Cdisplaystyle%5Clim%20_%7Bx%20%5Crightarrow%20%5Cinfty%7D%20%5Cfrac%7B%5Cleft(-%5Cfrac%7B1%7D%7B1%2Bx%5E%7B2%7D%7D%5Cright)%7D%7B%5Cfrac%7B%5Cpi%7D%7B2%7D-%5Ctan%20%5E%7B-1%7D%20x%7D%5C%2C%5C%2C%5C%2C%5C%2C

(using L' Hospital's rule)

%3D%5Cdisplaystyle%5Clim%20_%7Bx%20%5Crightarrow%20%5Cinfty%7D%20%5Cfrac%7B%5Cfrac%7B2%20x%7D%7B%5Cleft(1%2Bx%5E%7B2%7D%5Cright)%5E%7B2%7D%7D%7D%7B-%5Cleft(%5Cfrac%7B1%7D%7B1%2Bx%5E%7B2%7D%7D%5Cright)%7D%20%5C%2C%5C%2C%5C%2C%5C%2C

(using L' Hospital's rule)

%3D%5Cdisplaystyle%5Clim%20_%7Bx%20%5Crightarrow%20%5Cinfty%7D%20%5Cfrac%7B-2%20x%7D%7B1%2Bx%5E%7B2%7D%7D%3D0

%5CRightarrow%20y%3De%5E%7B0%7D%3D1

Chapter Questions
1 MCQs