Answer:
sec(4x) + C
Explanation:
original problem: ∫sec(4x)tan(x)dx
use integration by substitution (u-sub) by setting u = 4x
if u = 4x, then du/dx = 4 and du = 4dx (dx = du/4)
after substitution the integral is ∫sec(u)tan(u)(du/4)
move the 1/4 out of the integral by using the integral Constant rule to form 1/4∫sec(u)tan(u)du
the anti-derivative of sec(u)tan(u) is sec(u), memorize your trigonometric derivatives!!!!
after integration, we get sec(u)/4 + C , now plug u back into the equation
sec(4x) + C is the general solution
Answer: The last option.
Explanation: The precautionary principle would be considered to be most strictly applied where the precautionary measure is most disproportionate to the given risk. In all but the last option, there are either measures taken in response to concrete problems, or the precautionary measures are actually relaxed. In the last option, though, there are merely “fears” that antibiotics and growth hormones could cause harm (no experimental evidence), but the school board still takes the strict precautionary measure of mandating that schools only serve organic milk.
