CUET Preparation Today
If $\underset{x→0}{\lim}(1+ax+bx^2)^{2/x}=e^3$, then |
a = 3, b = 0 a = 3/2, b 1 a = 3/2, b = 4 a = 2, b = 3 |
a = 3/2, b = 4 |
$\underset{x→0}{\lim}(1+ax+bx^2)^{2/x}=\underset{x→0}{\lim}(1+ax+bx^2)^{\frac{1}{ax+bx^2}\frac{2(ax+bx^2)}{x}}$ $=e^{\underset{x→0}{\lim}\frac{2(ax+bx^2)}{x}}e^{2a}=e^3⇒a=\frac{3}{2}$, b any real number. Hence (C) is the correct answer. |
