Question: Evaluate limx→0 (sin 8xtan 9x).


A ) 8
B ) 89
C ) 1 / 9
D ) 98

Steps to derive

1 limx→0 (sin 8xtan 9x) = limx→0 (sin 8xxtan 9xx)
 [Divide the numerator and the denominator by x.]

2 = limx→0 (sin 8xx)limx→0 (tan 9xx) = 89
 [Use the formula limx→0sin mxx = m, limx→0tan nxx = n.]



Hence the right answer is Option B

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