document.write( "Question 1090295: find the limit of
\n" ); document.write( "(sin 2x)/(3x)find the limit of lim x-> 0 (sin 2x)/(3x) \n" ); document.write( "

Algebra.Com's Answer #704731 by MathLover1(20850) $\"\"$ $\"About$

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$\"lim%28x-%3E0%2C%28sin%282x%29%29%2F%283x%29%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "Move the term $\"1%2F3\"$ outside of the limit because it is constant with respect to $\"x\"$ .\r
\n" ); document.write( "\n" ); document.write( " $\"%281%2F3%29lim%28x-%3E0%2C%28sin%282x%29%29%2Fx%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "Evaluate the limit of the numerator and the limit of the denominator:
\n" ); document.write( "you got
\n" ); document.write( " $\"0%2F0+\"$ \r
\n" ); document.write( "\n" ); document.write( "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.\r
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\r
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\n" ); document.write( "\n" ); document.write( " $\"%281%2F3%29lim%28x-%3E0%2C2cos%282x%29%2F1%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%281%2F3%29%2A2cos%282lim%28x-%3E0%2Cx%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%281%2F3%29%2A2cos%282%2A0%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%281%2F3%29%2A2cos%280%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%281%2F3%29%2A2%2A1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2%2F3\"$ \r
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\n" ); document.write( "\n" ); document.write( "so, $\"lim%28x-%3E0%2C%28sin%282x%29%29%2F%283x%29%29=2%2F3+\"$
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