document.write( "Question 370647: Find a non-zero value for the constant “k” so that
\n" ); document.write( "f(x)=(tan(kx))/x when x<0 and
\n" ); document.write( "f(x)=3x+2k^2 when x>0 and
\n" ); document.write( "the function is continuous at x=0 \n" ); document.write( "

Algebra.Com's Answer #264227 by robertb(5830) $\"\"$ $\"About$

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The left-hand limit for f(x) is of the form 0/0, and so use L'Hopitals Rule: Get the limit of $\"k%28sec%28kx%29%29%5E2%2F1+\"$ as x approaches 0 from the left. The left hand limit is then equal to k. The right-hand limit as x approaches 0 is $\"2k%5E2\"$ .
\n" ); document.write( "Thus $\"2k%5E2+=+k\"$ , (by condition of continuity)
\n" ); document.write( "or k = 0 or 1/2. Discard the value k = 0.
\n" ); document.write( "Then the answer is k = 1/2. \n" ); document.write( "

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