Let [x] be the greatest integer les...
Question

# Let [x] be the greatest integer less than or equals to x. Then, at which of the following point(s) the function f(x)= XCOSA(*+]) is continuous? A X= 2 B x=1 x=-1 x=0

JEE/Engineering Exams
Maths
Solution
200
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( f(x)=x cos (x(x+[x))) ) begin{tabular}{l|c} ( ln 5 ) & ( lim _{x rightarrow+infty} x cos (x(x+2)) ) ( =lim _{x rightarrow 2^{+}} x cos (x(x+1) ) & ( log 2 cos (4 x) ) ( Rightarrow 2 cos (3 x) ) & 2 end{tabular} ( therefore ) Not continious At ( x=1 ) ( lim _{x rightarrow 1^{-}} x cos (pi(x+0)) lim _{x rightarrow++} x cos (pi(x+1)) ) ( 1 cos (x) quad-1 quad 1(cos (2 pi) ) Not conninions ( A+x=0 )