lecture15

# lecture15 - x ) = 2) d dx (cos x ) = 3) d dx (tan x ) = 4)...

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Lecture 15: Derivatives of Trigonometric Functions (Sec. 3.3) ex. Find the following limits: 1) lim ± ! 0 sin ± = 6 - ? ± 2) lim ± ! 0 cos ± = 6 - ? ±

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Consider the following important limit: lim ± ! 0 sin ± ± = 1
We can then evaluate: lim ± ! 0 cos ± ± 1 ± Evaluate the following limits: ex. lim x ! 0 sin 5 x x

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ex. lim x ! 0 sin 2 ( ±x ) 3 x 2 ex. lim x ! 0 sin 3 x tan 3 x
Evaluate the limits: ex. lim x ! 0 cos x ± 1 sec x ± 1 = ex. lim x ! 0 sin x 1 ± cos x

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Evaluate the following limits using substitution: ex. lim x ! ± 2 sin(cos x ) cos x ex. lim x ! ± sin x x ± ±
ex. Consider the function f ( x ) = ( sin x x < 0 cos x ± 1 x ² 0 Is f ( x ) continuous at x = 0? Is f ( x ) di±erentiable at x = 0?

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Derivatives of Trigonometric Functions 1) d dx (sin

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Unformatted text preview: x ) = 2) d dx (cos x ) = 3) d dx (tan x ) = 4) d dx (cot x ) = 5) d dx (sec x ) = 6) d dx (csc x ) = ex. Evaluate: d dx ( x sin x ) ex. Find the equation of the tangent line to f ( x ) = 4 x tan x at x = 4 . ex. Let f ( x ) = 1 tan x sec x . Find f ( x ) and each x-value for which the graph of f has a horizontal tangent line. Additional Examples Evaluate the limits: ex. lim x ! tan x 3 p x lim x ! 2 cos x x 2...
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## This note was uploaded on 02/10/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.

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lecture15 - x ) = 2) d dx (cos x ) = 3) d dx (tan x ) = 4)...

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