Evaluate the limit 1-cos(6x)/3x as x tends to zero?


2 Answers

David Torgerson Profile
David Torgerson answered
The because(6x) as x tends to 0 is 1.                       Substitute 1 for because(6x) term

The 3x as x tends to 0 is 0.                               Substitute x for 3x term

The term 1/x as x tends to 0 is infinity                 substitute infinity for because(6x)/3x

Thus   1 - (infinity) tends to - infinity.
Oddman Profile
Oddman answered
The limit of the expression you have written is
  1 - (1/3)*0 = 1

I assume you are concerned with the limit of

Evaluating this expression at x=0 gives the indeterminate form 0/0, so we apply L'Hopital's rule. We divide the derivative of the numerator by that of the denominator and evaluate again
  d(1-because(6x))/d(3x) = 6Sin(6x)/3
At x = 0, this is 0/3 = 0.

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