a) Prove that the function In(x + 1) is continuous at x = 0. You can...

 

Transcribed Image Text:

a) Prove that the function In(x + 1) is continuous at x = 0. You can use without proof that (In(x + 1))'= for x > -1. 2+1 b) Prove that there exists a point c (0, 1) such that 1 (7 marks) C 3. (In(4) - In(3)) You can only use without proof i) and ii) below. i) In(z) is differentiable for all r > 0. ii) Rolle's Theorem. (7 marks) c) State whether the following series converge or not. Justify your answer. n=1 n + n (n+1)2 ii) 1. n" + n a) Prove that the function In(x + 1) is continuous at x = 0. You can use without proof that (In(x + 1))'= for x > -1. 2+1 b) Prove that there exists a point c (0, 1) such that 1 (7 marks) C 3. (In(4) - In(3)) You can only use without proof i) and ii) below. i) In(z) is differentiable for all r > 0. ii) Rolle's Theorem. (7 marks) c) State whether the following series converge or not. Justify your answer. n=1 n + n (n+1)2 ii) 1. n" + n

Answer rating: 100% (QA)

a To prove that Inx 1 is continuous at x 0 we need to show that limo lnx 1 In01 ln1 10 lnx 1 l... View the full answer