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7.6-LHospital

7.6-LHospital - MthSc 108-Learning Activity Section 7.6...

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Unformatted text preview: MthSc 108-Learning Activity Section 7.6: Indeterminate Forms and L’Hopital’s Rule Solutions 1. lim x →∞ x ln x x + ln x = ∞ ∞ lim x →∞ ln x + 1 1 + 1 x = ∞ + 1 1 + = ∞ Thus lim x →∞ x ln x x + ln x = ∞ and the limit does not exist. 2. lim x → π- x- π ( ) tan x 2 type ∞ ⋅ lim x → π- x- π ( ) tan x 2 2 2 1 1 2 csc 2 1 1 lim 2 cot lim 2- =- = - = - =- →- → x x x x x π π π lim x → π- x- π ( ) tan x 2 = - 2 3. lim θ → 1 1- cos θ- 2 sin 2 θ type ∞- ∞ lim θ → 1 1- cos θ- 2 sin 2 θ - - + + = → θ θ θ θ θ 2 sin 2 cos 1 1 cos 1 cos 1 lim cos 2 1 lim cos sin 2 sin lim sin 1 cos lim sin 2 cos 1 cos 1 lim 2 2 2- =- = - = - - + = → → → → θ θ θ θ...
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7.6-LHospital - MthSc 108-Learning Activity Section 7.6...

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