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

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(5830) (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 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 .
Thus , (by condition of continuity)
or k = 0 or 1/2. Discard the value k = 0.
Then the answer is k = 1/2.
RELATED QUESTIONS
given f(x)=(x^3-4x^2+kx-2k)/ (x-5) find the value of k so that the remainder =... (answered by fractalier)

The function f is such that f(x) = 3x - 2 for x >= 0. The function g is such that g(x) = (answered by robertb)

{{{f(x) = x^3 +6x^2 + kx -4 }}} For what value of k will it have the same remainder... (answered by Theo)

Find "k" so when x^3 + kx^2 - kx + 1 is divided by x-2, the remainder is... (answered by drk)

Given the equation kx^2+(k-1)x+2k+3=0 where k is a non-zero integer, find the value of k... (answered by josmiceli)

Hello to all! I have been tackling this problem for the past 4 hours, and sadly with no... (answered by greenestamps,ikleyn)

The cubic polynomial f(x) is such that the coefficient of x^3 is -1 and the roots of the... (answered by KMST)

find the value of k. x^2+kx-21=0 when one root is... (answered by checkley77)

Assume that x=2 is a zero of f(x)=x^2+3kx+2k^2 (that is, f(2)=0). Find the value(s) of k. (answered by jim_thompson5910)