please show workexplanation 1C lim x rightarrow 0 xtan 4xSol

please show work/explanation!

[#1C]

Solution

at x = 0, tan 4x = 0, so we have a 0/0 form and use L\'Hopital\'s rule and find derivatives of top and bottom:

lim(x0) x / tan 4x = lim(x0) 1 / (4 sec² 4x) = lim(x0) ¼ cos² 4x = ¼•1 = ¼