Section 3.4 Derivatives of trigonometric functionsTheorem. limθ→0sin θ = 0.Theorem. limθ→0cos θ = 1.Theorem. limθ→0sin θθ= 1Corollary. limθ→0cos θ − 1θ= 0.Example 1. Find each limit(a.) limx→01 − cos 2x2x2(b.) limx→0sin 5x2x(c.) limx→0sin 4xsin 3x1(d.) limx→0tan 3xsin 2xDerivativesddxsin x = cos xddxcos x = − sin xddxtan x =1cos2x= sec2xddxcot x = −1sin2x= − csc2xddxcsc x = − csc x cot xddxsec x = sec x tan xExample 2. Finddydx(a.) y = cos x − 2 tan x(b.) y = 2x(√x − cot x)2(c.) y = x csc xExample 3. Find the points on the curve y =cos x2 + sin xat which the tangent is
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