What is the complete sequence of topics in the final exam of Mathematical Analysis I at the National Technological University, held on March 6, 2012?
A)1) Definition of Continuous Function and Discontinuities: classification.
A)2) Analysis of the continuity of a function.
B)1) Analysis of: domain, asymptotes, extreme points, inflection points, growth-decrease intervals, concavity intervals, image and graph, for the function.
B)2) Approximate calculation, using differentials, of the value of f(26) for the function in item B1). Estimate the error compared to the value obtained with a calculator.
C)1) Enunciation, in a complete, precise and detailed way, of the Mean Value Theorem of Integral Calculus. Geometric interpretation.
C)2) Determine if there is more than one real value c that satisfies the Intermediate Value Theorem of Integral Calculus for the function f(x) = in the interval [-1; 2]. Make the graph of the function and the rectangle that equals the area under the curve in the given interval.