JEE Main202324 Jan 2023Morning ShiftMathematicsLimitsActual
lim t → 0 1 1 sin 2 t + 2 1 sin 2 t + 3 1 sin 2 t . . . . . . n 1 sin 2 t sin 2 t is equal to
Options
- An 2 + n
- Bn
- Cn n + 1 2
- Dn 2
Correct answer
B. n
Step-by-step solution
L = lim t → 0 1 1 sin 2 t + 2 1 sin 2 t + 3 1 sin 2 t . . . . . . n 1 sin 2 t sin 2 t = lim t → 0 1 cosec 2 t + 2 cosec 2 t + 3 cosec 2 t . . . . . . n cosec 2 t sin 2 t = lim t → 0     n sin 2 t sin 2 t 1 n cosec 2 t + 2 n cosec 2 t + 3 n cosec 2 t . . . . . . 1 sin 2 t = n lim t → 0     0 + 0 + 0 . . . . . . 1 0 = n