Lim (tanx) / 2x as x approaches 0

You have to use L'Hospital Rule. So you take the derivative of the top then you take the derivative of the bottom.

1/2 * (lim x→0 (sec²x/1))

Substitute in the x-value

1/2 * (lim x→0 (sec² (0) / 1))

(lim x→0 (sec² (0) / 1) = 1

1/2 * 1

1/2