JEE Main 202226 Jul, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002Let β=limx→0αx−(e3x−1)αx(e3x−1)\beta=\mathop {\lim }\limits_{x \to 0} \frac{\alpha x-\left(e^{3 x}-1\right)}{\alpha x\left(e^{3 x}-1\right)}β=x→0limαx(e3x−1)αx−(e3x−1) for some α∈R\alpha \in \mathbb{R}α∈R. Then the value of α+β\alpha+\betaα+β is :AOption A. 145\frac{14}{5}514BOption B. 32\frac{3}{2}23COption C. 52\frac{5}{2}25DOption D. 72\frac{7}{2}27CheckSkip · show solution
