SOLUTION: find the limit of (sin 2x)/(3x)find the limit of lim x-> 0 (sin 2x)/(3x)

Algebra ->  Finance -> SOLUTION: find the limit of (sin 2x)/(3x)find the limit of lim x-> 0 (sin 2x)/(3x)      Log On


   

Question 1090295: find the limit of
(sin 2x)/(3x)find the limit of lim x-> 0 (sin 2x)/(3x)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
lim%28x-%3E0%2C%28sin%282x%29%29%2F%283x%29%29+
Move the term 1%2F3 outside of the limit because it is constant with respect to x.
%281%2F3%29lim%28x-%3E0%2C%28sin%282x%29%29%2Fx%29+
Evaluate the limit of the numerator and the limit of the denominator:
you got
0%2F0+
Since 0%2F0 is of indeterminate form, apply L'Hospital's Rule. L'Hospital's Rule states that the limit of a quotient of functions is equal to the limit of the quotient of their derivatives.


%281%2F3%29lim%28x-%3E0%2C2cos%282x%29%2F1%29
%281%2F3%29%2A2cos%282lim%28x-%3E0%2Cx%29%29
%281%2F3%29%2A2cos%282%2A0%29
%281%2F3%29%2A2cos%280%29
%281%2F3%29%2A2%2A1
2%2F3

so, lim%28x-%3E0%2C%28sin%282x%29%29%2F%283x%29%29=2%2F3+