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emmceceechavega
emmceceechavega emmceceechavega
  • 30-07-2016
  • Mathematics
Answered

Limit as x approaches pi/2 of cos(x)/x-(pi/2)

Verified Answer :

Hussain514 Hussain514
  • 03-08-2016

plug in x=0 gives 0/0. This is one of the indeterminate forms (some others are ∞/∞ and 0·∞) use L'Hospital's Rule. 
Differentiate the top and bottom of the fraction: 
lim (cos x) / (x - π/2) => lim (-sin x) / (1 - 0) 
Now you can substitute x = π/2 without problem 
lim = -1/1= -1

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