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This document contains solutions to two analysis questions. Question 1 asks to prove uniform convergence of the sequence of functions fn(x)=2/(2n)ln(1+nx) on the interval [1,2]. The solution shows the functions converge pointwise to 0 and satisfy the Cauchy criterion for uniform convergence. Question 2 considers the sequence of functions fn(x)=1/(1+x^2n) on [-∞,∞] and determines it converges pointwise but not uniformly as the pointwise limit is not continuous.
- Author
- Aiman khan
- Language
- EN