Newbetuts

If nonnegative $f: [0,1] \rightarrow \mathbb{R}$ has a continuous $f''$, then $\int_0^1 \Big| \frac{f''(x)}{f(x)} \Big| \,dx >4$

If $f$ is continuous and $f(x+y) = f(x)+f(y)$, then $f(x) = cx$ for all $x \in \mathbb{R}$

Can I apply the sequential criterion of continuity here?

what is sine of a real number

Existence of continuous angle function $\theta:S^1\to\mathbb{R}$

If $f$ is uniformly continuous on two sets, show that $f$ is also uniformly continuous on the union of two given sets

How does this discontinuity occur in evaluating a nested square root?

Continuity of absolute value of a function

Function $f(x)=\int_0^\infty\left|\sin(t)\cdot\sin(x\,t)\cdot e^{-t}\right|\,dt$

Show a function for which $f(x + y) = f(x) + f(y) $ is continuous at zero if and only if it is continuous on $\mathbb R$

Monotonic function satisfying darboux property $\Rightarrow$ continuous

Under what conditions does the limit f(g(x)) exist?

Prove that exists $x\in[0,2]$ such that $f(x)=\frac{1}{x}$. [duplicate]

$f:\mathbb R\to\mathbb R$ continuous function. Which of the following sets can not be image of $(0,1]$ under $f$?

Coming up with an example, a function that is continuous but not uniformly continuous

New posts in continuity

If $f$ is continuous & $\lim_{|x|\to {\infty}}f(x)=0$ then $f$ is uniformly continuous or NOT?

Remark 4.31 in Baby Rudin: How to verify these points?

Is every convex function on an open interval continuous? [duplicate]

Confusion on inequality in proof

Is a differentiable function on $(-2, 4)$ always integrable on $[-2, 4]$?

If nonnegative $f: [0,1] \rightarrow \mathbb{R}$ has a continuous $f''$, then $\int_0^1 \Big| \frac{f''(x)}{f(x)} \Big| \,dx >4$

If $f$ is continuous and $f(x+y) = f(x)+f(y)$, then $f(x) = cx$ for all $x \in \mathbb{R}$

Can I apply the sequential criterion of continuity here?

what is sine of a real number

Existence of continuous angle function $\theta:S^1\to\mathbb{R}$

If $f$ is uniformly continuous on two sets, show that $f$ is also uniformly continuous on the union of two given sets

How does this discontinuity occur in evaluating a nested square root?

Continuity of absolute value of a function

Function $f(x)=\int_0^\infty\left|\sin(t)\cdot\sin(x\,t)\cdot e^{-t}\right|\,dt$

Show a function for which $f(x + y) = f(x) + f(y) $ is continuous at zero if and only if it is continuous on $\mathbb R$

Monotonic function satisfying darboux property $\Rightarrow$ continuous

Under what conditions does the limit f(g(x)) exist?

Prove that exists $x\in[0,2]$ such that $f(x)=\frac{1}{x}$. [duplicate]

$f:\mathbb R\to\mathbb R$ continuous function. Which of the following sets can not be image of $(0,1]$ under $f$?

Coming up with an example, a function that is continuous but not uniformly continuous