Limits, Continuity & Differentiability
General
Grade 12
Question:
<p>If limx→0(1 + ax + bx2)2/x = e3, then:</p>
a = 3/2, b \in R
a = 3/2, b \in R+
a = 0, b = 1
a = 1, b = 0
Step-by-Step Solution
Key Concept: General
<p>Limit = elimx\to 0 2</p> x(ax+bx2) = e2a. Given e2a = e3 =\Rightarrow 2a = 3 =\Rightarrow a = 3/2. The term 2bx vanishes regardless of b.
Correct Answer: 1