Limits, Continuity & Differentiability
General
Grade None
Question:
<p>If f(x) is a polynomial of least degree such that limx→0
1 + f(x)+x2
x2
1/x
= e2, then f(2) is:</p>
Step-by-Step Solution
Key Concept: General
<p>Limit = elimx\to 0</p> f(x)+x2 x3 = e2 =\Rightarrow \lim_{x \to 0} f(x)+x2 x3 = 2. For least degree polynomial, f(x) + x2 = 2x3 =\Rightarrow f(x) = 2x3 -x2. f(2) = 2(8) -4 = 12.
Correct Answer: 4