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Vikash Nagar Grade: 12
        Lim gif of tanx by x  as x tend to 0
6 years ago

Answers : (1)

Askiitians Expert Mohit Singla
19 Points
										

Dear Vikash,


lim x-->0 [tan x /x] where [] is the greatest integer function(gif)
Considering f(x)=tanx - x
f'(x)=secx^2 -1
     =tanx^2
Thus f'(x)>0
Thus it is an increasing function.
f(0)=0
So for x>0 f(x)>0
or tan x > x
or tan x /x >1


Thus value  of [tanx /x] as lim x-->0+ is 1,where [] is the greatest integer function(gif)



[tanx /x] as lim x-->0- is also 1 as -ve sign in both the numerator as well as denominator


gets cancelled out.


Thus Lim x-->0+ [tan x /x]= lim x-->0- [tan x /x]= 1.



Please feel free to post as many doubts on our discussion forum as you can. If you find any


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Difficult to understand - post it here and we will get you the answer and detailed solution


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are all IITians and here to help you in your IIT JEE preparation.



All the best VIKASH !!!


 



Regards,


Askiitians Experts


MOHIT

6 years ago
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