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MATH1151 week3c3 - Week 3 Friday 11-12 Class Time allowed...

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Time allowed: 15 minutes. 1. (2 marks) Use logarithmic differentiation to find d dx x sin x for x > 0. 2. (2 marks) By expanding ( x y ) 2 prove that x 2 + y 2 2 xy for all real numbers x, y . Hence, or otherwise, determine the minimum value of y = x 6 + 1 x 6 . 3. (1 mark) Find the exact value of sin 1 sin 200 π 3 . 4. (5 marks) (a) Given that cosh( A + B ) = sinh A sinh B + cosh A cosh B , find a formula for cosh 2 x . By differentiation or otherwise, find a formula for sinh 2 x . (b) Using the results of part (i), express cosh 3 x as a cubic polynomial in cosh x . Hence, or otherwise, find cosh 3 x . Week 3 Friday 11-12 Class
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