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`        Lim gif of tanx by x  as x tend to 0`
7 years ago

19 Points
```										Dear Vikash,
lim x-->0 [tan x /x] where [] is the greatest integer function(gif)Considering f(x)=tanx - xf'(x)=secx^2 -1     =tanx^2Thus f'(x)>0Thus it is an increasing function.f(0)=0So for x>0 f(x)>0or tan x > xor 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
question Difficult to understand - post it here and we will get you the answer and detailed solution
All the best VIKASH !!!

Regards,
MOHIT
```
7 years ago
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