Applications of Differential Calculus Exercise

# Applications of Differential Calculus Exercise -...

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Application of Differential Calculus A-Level Pure Mathematics Chapter 5 Application of Differential Calculus Exercise 5A (L’Hospital’s Rule) Date : Name : ________________ 1. Evaluate 3 0 sin lim x x x x - 2. Evaluate the following limits: (a) 2 0 cos 1 lim x x x - (b) x x x 2 0 sin lim (c) x nx x sin sin lim 0 3. Evaluate the following limits: (a) x x x sin 0 lim + (b) 2 0 1 sec lim x x x - (c) 2 2 0 sin lim x x x 1

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Application of Differential Calculus 4. Evaluate the following limits: (a) x x x cos sin 1 lim 2 - π (b) - x x x tan 1 1 lim 0 (c) 3 0 tan lim x x x x - 5. Evaluate the following limits: (a) x x x x x sin tan lim 2 0 - (b) x x x x e 1 0 ) ( lim + (c) x x x + ∞ 2 cos lim Ans: 1 . 6 1 2 . 2 1 , 0 , n 3 . 1, 2 1 , 1 4 . 0, 0, 3 1 - 5 . 3 1 , 2 e , 1 2
Application of Differential Calculus A-Level Pure Mathematics Chapter 5 Application of Differential Calculus Exercise 5B (L’Hospital’s Rule) Date : Name : ________________ 1 Evaluate the following limits: (a) x x e x 1 0 )] [ln( lim + (b) x x x ln 1 0 ) (sin lim + 2. Evaluate: (a) 5 1 1 1 lim x x x - - (b) ) tan (sec lim 2 x x x - π [HKAL 1994] 3. Evaluate: 3

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Application of Differential Calculus (a) 2 0 sin 1 lim x x e x x - - (b) x x x e 1 0 5 2 3 lim + [HKAL 1998] Ans: 1 . e e 1 , e 2 . 2 5 , 0 3 . 2 1 , 5 3 e A-Level Pure Mathematics 4
Application of Differential Calculus Chapter 5 Application of Differential Calculus Exercise 5C (Monotonic Functions) Date : Name : ________________ 1. Show that the function 3 tan ) ( 3 x x x x f - - = is strictly increasing for

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Applications of Differential Calculus Exercise -...

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