Name: Real Analysis by Dr. AllaganDate: Assignment #4Instruction: Use Latex or clearly hand write...

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Name: Real Analysis by Dr. AllaganDate: Assignment #4Instruction: Use Latex or clearly hand write your solutions to the following problems. Submit/Upload youanswers as a JPEG, PNG, WORD, or PDF file.Question 1Show (use N − �) that the following sequence converges to a real value L, after you find L using limits:(√n2 + 1− n)Question 2Let xn :=1ln(n+ 1)for n ∈ N.(a) Use the definition of limit to show that limn→∞(xn) = 0(b) Find a specific value of N(�) as required in the definition of limit, when:(i) � = 1/2 and(ii) � = 1/10.1 of 1

Rajeswari · Accepted Answer

Real analysis
Consider M =
Before finding limits let us simplify the expression by multiplying with conjugate.
M = 
Let N>n
Then we have M =  since N is positive
M n, we have
|M-0|M, we have
i.e. 
Hence limit is 0.
b)
(i) We must have| m
Rewrite the inequality as
,

Name: Real Analysis by Dr. Allagan Date: Assignment #4 Instruction: Use Latex or clearly hand write your solutions to the following problems. Submit/Upload your answers as a JPEG, PNG, WORD, or PDF...

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