contestada

Find the limit, use l'hospitals rule where appropiate. If there is a more elementary method, consider using it. lim \theta ->(\pi )/(2) (1-sin(\theta ))/(1+cos(6\theta ))

Respuesta :

Answer

θ approaches π/2

numerator = (1 - sin(θ))

denominator = (1 + cos(6θ))

lim (θ -> π/2) (1 - sin(θ)) / (1 + cos(6θ))  (L'Hospital's)

= lim (θ -> π/2) -cos(θ) / -6sin(6θ)

= -cos(π/2) / -6sin(6 x π/2)

= 0 / 0 (denominator = (1 + cos(6θ)))

= lim (θ -> π/2) sin(θ) / 36cos(6θ)

= sin(π/2) / 36cos(6 x π/2)

= 1/-36

limit (θ -> π/2) [(1 - sin(θ)) / (1 + cos(6θ))] = -1/36

Otras preguntas