Maths WorkshopMaths problems with full solutions

Continuity

12 problems · Continuity of functions of several variables.

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Ex.34Summary of continuity

#summary #continuity

Ex.77Continuity of a rational function

#rational function #domain #continuity

Ex.107Coordinate projections are continuous

#projection #continuity #coordinates

Ex.225Continuity of a polynomial

#continuity #polynomial #continuity everywhere

Ex.864A discontinuous function with bounded values

#discontinuity #bounded #counterexample

Ex.865Discontinuity via two paths

#discontinuity #paths #limits

Ex.866Norm and distance are continuous

#norm #distance #continuity

Ex.867Continuity of a piecewise function

#piecewise #continuity #xy

Ex.868Continuity via polar coordinates

#polar #continuity #bound

Ex.869Continuous extension

#continuous extension #removable singularity

Ex.1601Image of a compact set under a continuous function

#compactness #continuous image #extrema

Ex.1602A function that is not continuous despite radial limits

#continuity #radial limit #counterexample