document.write( "Question 365859: Evaluate the following limits or show they do not exist:
\n" ); document.write( "a) lim x→0 $\"+%28sin%28x%29%29%5E2%2F%28x%281-cos%28x%29%29%29++\"$
\n" ); document.write( "b) lim x→0 $\"++%28sin%28ax%29%29%2F%28sin%28bx%29%29+\"$ where a,b are nonzero real numbers
\n" ); document.write( "c) lim x→1 $\"+%28x%5E3-1%29%2Fabs%28x%5E3-1%29+\"$
\n" ); document.write( "d) lim x→2 $\"+%281-2%2Fx%29%2F%281-4%2Fx%5E2%29+\"$ \n" ); document.write( "

Algebra.Com's Answer #260780 by robertb(5830) $\"\"$ $\"About$

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b) Answer is a/b, by L'Hopital's rule.
\n" ); document.write( "c) Limit does not exist: left and right hand limits are not the same. Right hand limit is 1, while the left hand limit is -1.
\n" ); document.write( "d) $\"+%281-2%2Fx%29%2F%281-4%2Fx%5E2%29+=+1%2F%281%2B2%2Fx%29+\"$ . Therefore the limit is $\"+1%2F%281%2B2%2F2%29+=+1%2F%281%2B1%29+=+1%2F2+\"$ \n" ); document.write( "

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