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Published byAbner Ball Modified over 9 years ago
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If is measured in radian Then: If is measured in radian Then: and: - <1-cos < - < sin <
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From the theorem, and by sandwich theorem, We find that a) - < < 0 0 0As sin= 0
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And b)- < 1-cos <so 0 0 0 As 1-cos =0 Cos = 1
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Example Find the limit if it exists:
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Example g( )=1 h( )= cos
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Example & therefore…
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If we graph, it appears that
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Find the following limits: a) Put = 3x so as x 0, = 3x 0 1 = = Solution
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b) = = = Solution
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Put = sin x so as x 0, = sin x 0 = Find ==1 Solution
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Find: = = = = = = Solution
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1) Find = Put = t- so as t, 0. = 1 = Solution
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Derivative of y = sin x WHY?
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= 0 +cos(x)*1 = cos (x)
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Derivative of Sine, Cosine
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Examples: f(x) = x 2 +sin(x) f’(x) = 2x + cos(x) f(t) = cos(t) – 5t -2, then f '(t) = -sin (t) +10t -3 Derivative of Sine, Cosine
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Find tan x tan x = = = Solution
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Derivatives of Trigonometric Functions
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Find if : 1) Y= Solution
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2) Y = Find y’ if y = Solution
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Find: = ==
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Has a tangent at x = 0. Show that the function : F(x) = X 0 X = 0
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Find the values of a and b s.t the function : F(x) =, x 2, x < 2 Is diff. Every where.
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