We have to find the the greatest integer part of the value [sinx]. we know that sin pi/2 = 1 but since the limit is approaching pi/2 but is not completely pi/2, therefore we can conclude by the rules of greatest integer function that the value of function greater than 0 and slightly less than 1 is always zero(only if it is the greatest integer function).
When we consider the value of sin[pi/2] it gets in between 0 and 1. And we know that, [ ] this bracket indicates the greatest integer function. therefore,when we consider the both left hand limit and right hand limit they both equal each other to 0. that's why 0 is the correct answer.
Actually sinπ/2 is 1, but the question is greatest integer function of sinx i.e, [sinx] and the value is not exactly 1 as limit approaches π/2 and not exactly π/2. So it is to be considered as 0 by the greatest integer function rule. So answer is 0. Option C is correct.
Sin(x) tending to 90° means either greater than 90° or less then 90° in both the cases it will less the zero according to it's graph hence gif of any number less the one is absolute zero. good question
The question really mean that if x approach 90*then sinx approach what, yes it approach 1,but not exactly 1,it may be 0.99 something ,you may think it may be 1.01 but sin value doesn't exceed 1.so G.I.F of less than one is zero
Just see limit is in greatest integer function , since range of sinx is -1 to 1 .From graph you can see when you see left hand limit you got a number less than 1 whose greatest integer is zero(0) similarly when you see right hand limit you got a number less than 1 whose greatest integer is zero(0) SINCE RHL=LHL=0 SO LIMIT OF FUNCTION EXISTS AT pi/2 and equal to zero(0)
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