Answer: To apply l'Hospital's Rule, we need to take the derivative of the numerator and denominator separately with respect to θ.
Taking the derivative of the numerator:
d/dθ [1 - sin(θ)] = -cos(θ)
Taking the derivative of the denominator:
d/dθ [1 + cos(6θ)] = -6 sin(6θ)
Now we can apply l'Hospital's Rule by taking the limit of the ratio of the derivatives:
lim θ→π/2 (-cos(θ)) / (-6 sin(6θ))
When θ approaches π/2, cos(θ) approaches 0 and sin(6θ) approaches 1. Therefore, the limit simplifies to:
= 0 / (-6)
= 0
Hence, the limit of (1 - sin(θ)) / (1 + cos(6θ)) as θ approaches π/2 is 0.