Limits, Continuity & Differentiability
General
Grade 12
Question:
<p>If f(x) = cos 2−cos 2x
x2−|x|
, then:</p>
lim x→ 1 f(x) = 2 sin 2
lim x→ -1 f(x) = 2 sin 2
lim x→ -1 f(x) = 2 cos 2
lim x→ 1 f(x) = 2 cos 2
Step-by-Step Solution
Key Concept: General
<p>• Case x \to 1: f(x) = cos 2-cos 2x</p> x2-x . Use L’Hopital: lim 2 sin 2x 2x-1 = 2 sin 2. • Case x \to -1: f(x) = cos 2-cos 2x x2+x . Use L’Hopital: lim 2 sin 2x 2x+1 = -2 sin 2 -1 = 2 sin 2.
Correct Answer: (A, B)