MAT 301 Analysis 1 CA 2023

About this paper

MAT 301: University of Buea, Continuous Assessment II (13-12-2023, Dr Djiomba Sylvie): convexity/path-connectedness definitions and a disconnected-annulus sketch/classification; a sequential-continuity exercise for g(x,y)=x^2y/(x^4+y^2) at the origin, where the source's own guided bound is shown to only establish boundedness, not the limit 0 -- flagged and corrected using the classical y=x^2 counterexample to conclude g is in fact NOT continuous at the origin; gradient/divergence and linear approximation of a quadratic function; an epsilon-delta argument; a critical-point/Hessian/saddle-point analysis of x^m-y^n+z^p generalized via a direct axis-sign argument (the Hessian is degenerate for exponents above 2); a line-integral evaluated along a helical path (exam-taker's own handwritten working in the margin not transcribed).