JEE Main202229 Jun 2022Evening ShiftMathematicsLimitsActual
The value of lim x → 1 x 2 - 1 sin 2 π x x 4 - 2 x 3 + 2 x - 1 is equal to:
Options
- Aπ 2 6
- Bπ 2 3
- Cπ 2 2
- Dπ 2
Correct answer
D. π 2
Step-by-step solution
Given, lim x → 1 x 2 - 1 sin 2 π x x 4 - 2 x 3 + 2 x - 1 = lim x → 1 x 2 - 1 sin 2 π x x 2 - 1 x 2 - 2 x + 1 = lim h → 0 sin 2 π 1 + h 1 + h - 1 2 = lim h → 0 sin 2 π h h 2 = lim h → 0 sin π h π h 2 π 2 = π 2