Question

Limit as x approaches 0 of (tan7x)/(sin3x)

Answer 1

so... using L'Hopital rule, LH, since this one is a indeterminate type


`\bf \lim\limits_(x\to 0)~\cfrac{tan(7x)}{sin(3x)}\implies \underline{LH}\quad \lim\limits_(x\to 0)~\cfrac{7sec^2(7x)}{cos(3x)}\implies \cfrac{7\cdot (1)/(cos^2(7x))}{cos(3x)} \\\\\\ \lim\limits_(x\to 0)~\cfrac{7\cdot (1)/(cos^2(0))}{cos(0)}\implies \cfrac{7\cdot (1)/(1)}{1}\implies 7`