jee-main 2022 Q68

jee-main · India · session2_26jul_shift2 Sequences and series, recurrence and convergence Convergence proof and limit determination

Let $\beta = \lim _ { x \rightarrow 0 } \frac { \alpha x - \left( e ^ { 3 x } - 1 \right) } { \alpha x \left( e ^ { 3 x } - 1 \right) }$ for some $\alpha \in \mathbb { R }$. Then the value of $\alpha + \beta$ is:
(1) $\frac { 14 } { 5 }$
(2) $\frac { 3 } { 2 }$
(3) $\frac { 5 } { 2 }$
(4) $\frac { 1 } { 2 }$

Let $\beta = \lim _ { x \rightarrow 0 } \frac { \alpha x - \left( e ^ { 3 x } - 1 \right) } { \alpha x \left( e ^ { 3 x } - 1 \right) }$ for some $\alpha \in \mathbb { R }$. Then the value of $\alpha + \beta$ is:\\
(1) $\frac { 14 } { 5 }$\\
(2) $\frac { 3 } { 2 }$\\
(3) $\frac { 5 } { 2 }$\\
(4) $\frac { 1 } { 2 }$

Paper Questions

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