Question
Let $\beta=\mathop {\lim }\limits_{x \to 0} \frac{\alpha x-\left(e^{3 x}-1\right)}{\alpha x\left(e^{3 x}-1\right)}$ for some $\alpha \in \mathbb{R}$. Then the value of $\alpha+\beta$ is :
Let $\beta=\mathop {\lim }\limits_{x \to 0} \frac{\alpha x-\left(e^{3 x}-1\right)}{\alpha x\left(e^{3 x}-1\right)}$ for some $\alpha \in \mathbb{R}$. Then the value of $\alpha+\beta$ is :