Question

If $\sqrt{3}$, then

• A. a = 3, b = 0
• B. a = 3/2, b ≠ 1
• C. a = 3/2, b = 4
• D. a = 2, b = 3

Answer 1

Answer: (C)

a = 3/2, b = 4

Answer 2

$\lim _ { x \rightarrow 0 } \left( 1 + a x + b x ^ { 2 } \right) ^ { 2 / x } = \lim _ { x \rightarrow 0 } \left( 1 + a x + b x ^ { 2 } \right) ^ { \frac { 1 } { a x + b x ^ { 2 } } } \frac { 2 \left( a x + b x ^ { 2 } \right) } { x }$

= $e ^ { \lim _ { x \rightarrow 0 } \frac { 2 \left( a x + b x ^ { 2 } \right) } { x } } = e ^ { 3 } \Rightarrow a = \frac { 3 } { 2 }$ b any real number