SOLUTION: Find a non-zero value for the constant “k” so that f(x)=(tan(kx))/x when x<0 and f(x)=3x+2k^2 when x>0 and the function is continuous at x=0

Algebra ->  Algebra  -> Inequalities -> SOLUTION: Find a non-zero value for the constant “k” so that f(x)=(tan(kx))/x when x<0 and f(x)=3x+2k^2 when x>0 and the function is continuous at x=0      Log On

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Question 370647: Find a non-zero value for the constant “k” so that
f(x)=(tan(kx))/x when x<0 and
f(x)=3x+2k^2 when x>0 and
the function is continuous at x=0
Answer by robertb(4012) About Me  (Show Source):
You can put this solution on YOUR website!
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.
Thus 2k%5E2+=+k, (by condition of continuity)
or k = 0 or 1/2. Discard the value k = 0.
Then the answer is k = 1/2.