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Given : Lim x→π/6 (2sinx - 1) /(π - 6x)
To Find : Solve
Solution:
Lim x→π/6 (2sinx - 1) /(π - 6x)
Substituting x = π/6
2sinx - 1 = 2sin(π/6) - 1 = 2(1/2) - 1 = 0
π - 6x = π - 6(π/6) = 0
0/0 form
Hence apply L' Hosp rule
Take derivative of numerator and denominator separately
Lim x→π/6 (2cosx) /(-6)
=> Lim x→π/6 cosx /(-3)
Substituting x = π/6
= cosπ/6 /(-3)
= (√3 / 2) / (-3)
= -√3 / 6
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