Problem Set 06s

Lim lim x x 0 sin y sin x 2 sin x 2 lim x lim

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Unformatted text preview: n) Problem Set 06 Solution 3.3 Derivatives of Trigonometric Functions 3.4 Chain Rule GE 207C 4. Find the Limit: sin θ a. lim θ → 0 θ + tan θ Solution: sin θ sin θ sin θ θ θ lim = = θ →0 θ + tan θ tan θ sin θ 1 θ+ 1+ ⋅ θ θ cos θ 1 1 lim = θ →0 1 + 1 2 ( x ) when 1 1 + 3x sin x 2 x →0 x Solution: sin x 2 lim x →0 x b. lim = lim x x →0 ⎡ྎ ⎡ྎ sin y ⎤ྏ sin x 2 sin x 2 ⎤ྏ = lim x ⎢ྎlim 2 ⎥ྏ = (0)⎢ྎlim ⎥ྏ = 0(1) 2 x →0 x ⎣ྏ y →0 y ⎦ྏ ⎣ྏ x→0 x ⎦ྏ sin x 2 =0 x →0 x lim c. sin (x − 1) x →1 x 2 + x − 2 lim Solution: 3 Hung Nguyen Problem Set 06 Solution GE 207C 3.3 Derivatives of Trigonometric Functions 3.4 Chain Rule sin( x − 1) sin (x − 1) sin (x − 1) 1 g '( x ) = (3) ( x − 8) + (3x − 5) (1) lim 2 = lim = lim ⋅ lim x →1 x + x − 2 x →1 (x + 2 )(x − 1) x →1 x →1 x + 2 x −1 = 3x − 24 + 3x − 5 = 6 x − 29 = 0 = lim z →0 = sin( z ) 1 ⎛ྎ 1 ⎞ྏ ⋅ lim = (1)⎜ྎ ⎟ྏ x →1 x + 2 z ⎝ྎ 3 ⎠ྏ x= 1 3 d. lim t →0 To find the point y ⎛ྎ 29 ⎞ྏ g ⎜ྎ ⎟ྏ = −361 / 12 ⎝ྎ 6 ⎠ྏ tan 6t sin 2t (x, y ) = ⎛ྎ 29...
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This document was uploaded on 02/27/2014 for the course M 408c at University of Texas.

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