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if [.] denotes the greatest integer function then find the value of lim x tends to infinity ([x]+[2x]+.........[nx])/n^2 any help please?

if [.] denotes the greatest integer function then find the value of lim x tends to infinity ([x]+[2x]+.........[nx])/n^2
any help please?

Grade:12

1 Answers

sumanth
32 Points
6 years ago
 

ANS    3sinx+4cosx=5

 

     => 3/5 sinx +4/5 cosx = 1

 

     let cosA=3/5   => sinA=4/5

 

     =>  cosAsinx + sinAcosx = 1

 

     =>  sin(x+A) = 1

 

Now,

 

       4sinx - 3cosx

 

  =   5(4/5sinx - 3/5 cosx)     [multipying numerator and denominator by 5]

 

  =   5(sinAsinx - cosAcosx)

 

  =   -5{cos(x+A)} = -5[root{1-(sin(x+A)^2)}] = -5 x 0 = 0          Ans 0

 

 

 

TRICK: if asinx+bcosx is given then multiply numerator and denominator by root(a^2 +b^2)

 

            this method is useful  in many questions 

 

 

 

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