Find a non-zero value for the constant k that makes $f(x)=\begin{Bmatrix} \dfrac{\tan(kx)}{x} ,& x<0 \\[6pt] 3x+2k^{2}, & x\geqslant 0 \end{Bmatrix}$ continous at $x=0$.
I tried to do this question but I dont know how to begin this question.need some help
$$ \lim_{x\to0} \frac{\tan(kx)}{x} = \lim_{x\to0} \left( \frac{k}{\cos(kx)} \cdot\frac{\sin(kx)}{kx} \right) $$
The limit of the second fraction above should be familiar. The first has no $0$ in the denominator so it's routine. The limits of the two pieces in the definition of the function must be equal to each other.
