continuity and differentiability greatest integer function IIT Jam 2013 real analysis

Sequences, bounded sequence, limit of a sequence, convergent sequences, limit theorems, monotone sequences, monotone convergence theorem, subsequences, convergence and divergence criteria, existence of monotonic subsequences (idea only), Bolzano-Weierstrass theorem for sequences and sets, definition of Cauchy sequence, Cauchy's convergence criterion, limit superior and limit inferior of a sequence.

Definition of infinite series, sequence of partial sums, convergence of infinite series, Cauchy criterion, absolute and conditional convergence, convergence via boundedness of sequence of partial sums, tests of convergence: comparison test, limit comparison test, ratio test, Cauchy's nth root test alternating series, Leibniz test.

Functions of One Real Variable: Limit, continuity, intermediate value property, differentiation, Rolle’s Theorem, mean value theorem, L'Hospital rule, Taylor's theorem, maxima, and minima.

Real Analysis: Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets, completeness of R. Power series (of real variable), Taylor’s series, radius and interval of convergence, term-wise differentiation, and integration of power series.

continuity and differentiability right hand limit greatest integer function IIT Jam 2013 mathematics

En Jam MA 2013, 4
Key (c)

[nisharawat]

Amazing plz keep trying such great question u r doing great job

[rupamsingh]

Superb Sir, you are doing such a fantastic job