Limits, Continuity & Differentiability
General
Grade 12
Question:
<p>If f(x) is an odd linear polynomial with f(1) = 1, then limx→0 2f(tan x)−2f(sin x)
x2f(sin x)
is:</p>
Step-by-Step Solution
Key Concept: General
<p>f(x) is odd linear</p> =\Rightarrow f(x) = cx. f(1) = 1 =\Rightarrow c = 1 =\Rightarrow f(x) = x. Limit = \lim_{x \to 0} 2tan x-2sin x x2 sin x = lim 2sin x(2tan x-sin x-1) x2 sin x . Using at-1 t \to ln a: lim 1 \cdot (tan x-sin x) ln 2 x3 = lim (x3/2) ln 2 x3 = 1 2 ln 2.
Correct Answer: 3