MATH1014TutorialExerciseWeek4Answers - MATH1014 T02A T02B T02C T02D Tutorial Exercise(Week 4 Answers n b k 1 a Arc Length L lim 1 f xk 2 x n 1 1 f x 2

MATH1014TutorialExerciseWeek4Answers - MATH1014 T02A T02B...

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MATH1014 T02A / T02B / T02C / T02D Tutorial Exercise (Week 4) Answers Arc Length: bankkndxxfxxfL212*)(1)(1lim1.Find the arc length of the following curves on the given interval. 2xx, [1, 6] 24356ln3 (a)y=24ln3(b)y=2/12/33xx, [4, 16] 362(c)y=2/12/32132xx, [1, 9] 355 2.Define 2sinhzzeezand 2coshzzeez. Notice that sinh 0 = 0 and cosh 0 = 1. (a)Prove the Pythagorean identity 1sinhcosh22zz(b)Prove the differentiation formulas zzcosh)(sinhand zzsinh)(cosh(c)Given that y=1ln2xx, show that x= cosh (d)Find the arc length of the curve y=1ln2xxfor 1 x2. 3.What differentiable functions have an arc length on the interval [a, b] given by the following integrals? (a)badxx434)( . . y . 1 C

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