Question

Reconciling different definitions of differentiability in multi-dimensions.

score 190 · Answer 1 · 2026-04-15 00:13:36

190

Views

Reconciling different definitions of differentiability in multi-dimensions.

Published on 15 Apr 2026 - 0:13

score 287 · Answer 2 · 2026-04-14 06:09:32

287

Views

Did I find counter-example to "function continuous iff inverse image of every closed set is a closed set"

Published on 14 Apr 2026 - 6:09

score 213 · Answer 3 · 2026-04-17 04:30:10

213

Views

Prove that $f$ is uniformly continuous iff there exist sequences $a_n,b_n$ such that if $\lim a_n=\lim b_n \implies \lim f(a_n)=\lim f(b_n)$

Published on 17 Apr 2026 - 4:30

score 106 · Answer 4 · 2026-04-11 10:43:19

106

Views

existence of a function that is continuous at every rational and discontinuous at every irrational

Published on 11 Apr 2026 - 10:43

score 615 · Answer 5 · 2026-04-16 12:26:32

615

Views

Proving the limit of a function exists at one (and only one) point.

Published on 16 Apr 2026 - 12:26

score 159 · Answer 6 · 2026-05-10 14:55:52

159

Views

Proving uniform continuity of the exponential function on a semi-finite interval

Published on 10 May 2026 - 14:55

score 1.7k · Answer 7 · 2026-04-16 02:40:57

1.7k

Views

Prove that $f(x,y) = \sqrt{x^2 + y^2}$ is continuous at $a=(3,\frac{1}{2})$

Published on 16 Apr 2026 - 2:40

score 500 · Answer 8 · 2026-04-12 12:42:21

500

Views

basic definition of continuity in a closed interval

Published on 12 Apr 2026 - 12:42

score 47 · Answer 9 · 2026-04-08 22:40:50

47

Views

Continuous function composition

Published on 08 Apr 2026 - 22:40

score 33 · Answer 10 · 2026-04-11 14:13:43

33

Views

Continous function under the line $x=y$

Published on 11 Apr 2026 - 14:13

score 8.6k · Answer 11 · 2026-04-12 09:50:07

8.6k

Views

Values of k that make piecewise function continuous

Published on 12 Apr 2026 - 9:50

score 351 · Answer 12 · 2026-04-13 15:50:22

351

Views

Exception to the Sandwich/Squeeze principle

Published on 13 Apr 2026 - 15:50

score 190 · Answer 13 · 2026-04-15 17:38:55

190

Views

Show that if $f :[0,\infty[ \rightarrow\mathbb{R}$ is continous then $f$ attain a maximum.

Published on 15 Apr 2026 - 17:38

score 134 · Answer 14 · 2026-05-10 12:33:55

134

Views

Will any linear combination of degree 3 b-splines be C2 continuous?

Published on 10 May 2026 - 12:33

score 583 · Answer 15 · 2026-05-10 20:00:26

583

Views

affine functions and Lipschitz continuity

Published on 10 May 2026 - 20:00

List Question

Reconciling different definitions of differentiability in multi-dimensions.

Did I find counter-example to "function continuous iff inverse image of every closed set is a closed set"

Prove that $f$ is uniformly continuous iff there exist sequences $a_n,b_n$ such that if $\lim a_n=\lim b_n \implies \lim f(a_n)=\lim f(b_n)$

existence of a function that is continuous at every rational and discontinuous at every irrational

Proving the limit of a function exists at one (and only one) point.

Proving uniform continuity of the exponential function on a semi-finite interval

Prove that $f(x,y) = \sqrt{x^2 + y^2}$ is continuous at $a=(3,\frac{1}{2})$

basic definition of continuity in a closed interval

Continuous function composition

Continous function under the line $x=y$

Values of k that make piecewise function continuous

Exception to the Sandwich/Squeeze principle

Show that if $f :[0,\infty[ \rightarrow\mathbb{R}$ is continous then $f$ attain a maximum.

Will any linear combination of degree 3 b-splines be C2 continuous?

affine functions and Lipschitz continuity

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