If $\underset{x\to 0}{\lim }\frac{x+3\sin x-x^3-k \sin h x}{1-\cos x+x^2-3x^3}$ exists and is finite then the value of ‘k’ is

$$\begin{gathered} \underset{\mathrm{x}\to 0}{\lim }\frac{\mathrm{x}+3\mathrm{sinx}-{\mathrm{x}}^3-\mathrm{k} \sinh \mathrm{x}}{1-\cos \mathrm{x}+{\mathrm{x}}^2-3{\mathrm{x}}^3} \left(\frac{0}{0} \mathrm{form}\right) \\ =\underset{\mathrm{x}\to 0}{\lim }\frac{1+3\cos \mathrm{x}-3{\mathrm{x}}^3-\mathrm{k} \cos \mathrm{h} \mathrm{x}}{ \sin \mathrm{x}+2\mathrm{x}-9{\mathrm{x}}^2} \\ \mathrm{Dr} \to 0 \mathrm{Nr} \mathrm{also} \to 0 \\ 1+3-\mathrm{k}=0 \Rightarrow \mathrm{k}=4 \end{gathered}$$