formulae0111

formulae0111 - Elementary Differential and Integral...

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Elementary Differential and Integral Calculus FORMULA SHEET Exponents x a · x b = x a + b , a x · b x = ( ab ) x , ( x a ) b = x ab , x 0 = 1 . Logarithms ln xy = ln x + ln y , ln x a = a ln x , ln 1 = 0, e ln x = x , ln e y = y , a x = e x ln a . Trigonometry cos 0 = sin π 2 = 1, sin 0 = cos π 2 = 0 , cos 2 θ + sin 2 θ = 1, cos (− θ ) = cos θ , sin (− θ ) = − sin θ , cos ( A + B ) = cos A cos B sin A sin B , cos 2 θ = cos 2 θ sin 2 θ , sin ( A + B ) = sin A cos B + cos A sin B , sin 2 θ = 2 sin θ cos θ , tan θ = sin θ cos θ , sec θ = 1 cos θ , 1 + tan 2 θ = sec 2 θ . Inverse Functions y = sin 1 x means x = sin y and π 2 6 y 6 π 2 . y = cos 1 x means x = cos y and 0 6 y 6 π . y = tan 1 x means x = tan y and π 2 < y < π 2 . y = x 1 /n means x = y n . y = ln x means x = e y . Alternative Notation arcsin x = sin 1 x , arccos x = cos 1 x , arctan x = tan 1 x , log e x = ln x . Note:
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formulae0111 - Elementary Differential and Integral...

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