Question

Periodicity of $f$ such that $ f(x+2)=f(x-1)f(x+5)$

score 72 · Answer 1 · 2026-04-22 22:11:00

72

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Periodicity of $f$ such that $ f(x+2)=f(x-1)f(x+5)$

Published on 22 Apr 2026 - 22:11

score 534 · Answer 2 · 2026-04-15 23:54:41

534

Views

$X$ is the space of all continuous functions with the norm $||f||=\sup_{t\ge0}e^{kt}|f(t)|<\infty.$ Is $X$ a Banach space?

Published on 15 Apr 2026 - 23:54

score 486 · Answer 3 · 2026-04-25 04:55:54

486

Views

Integral inequality on decreasing function

Published on 25 Apr 2026 - 4:55

score 46 · Answer 4 · 2026-04-16 13:33:56

46

Views

Let $T \in L(\mathbb{R}^n,\mathbb{R}^m)$. Prove that $T$ is differentiable at every $x \in \mathbb{R}^n$.

Published on 16 Apr 2026 - 13:33

score 65 · Answer 5 · 2026-04-15 02:22:24

65

Views

Why the following constraint is non-convex? Is my explanation right or wrong?

Published on 15 Apr 2026 - 2:22

score 112 · Answer 6 · 2026-04-14 03:29:55

112

Views

Direct Relationship Between Second Derivative & Points of Inflection

Published on 14 Apr 2026 - 3:29

score 72 · Answer 7 · 2026-04-23 15:16:16

72

Views

If $f:[a,b]\to\mathbb{R}$ is a function of first class, does it mean that $f$ is continuous everywhere except countably many points in $[a,b]?$

Published on 23 Apr 2026 - 15:16

score 193 · Answer 8 · 2026-04-16 19:06:29

193

Views

Find all $f$ that satisfies $f:\mathbb{R}\rightarrow\mathbb{R};f(x+y)+f(x)f(y)=(1+x)f(y)+(1+y)f(x)+f(xy)$

Published on 16 Apr 2026 - 19:06

score 114 · Answer 9 · 2026-04-16 10:17:28

114

Views

Sequences unbounded above diverges?

Published on 16 Apr 2026 - 10:17

score 1.4k · Answer 10 · 2026-04-15 18:30:54

How? Consider function $f : \mathbb {R} \rightarrow \mathbb {R}$ defined as $f (x)=x^2 + 3$. Find $f ([-3,5])$ and $f^{-1} ([12,19])$.

score 57 · Answer 11 · 2026-04-14 03:50:10

57

Views

To prove an inequality of degree 3 polynomilals

Published on 14 Apr 2026 - 3:50

score 314 · Answer 12 · 2026-04-15 11:55:48

314

Views

Limits without L'Hopital $\lim\limits_{x\to 0} \frac{e^{3x}-e^{-4x}}{\sin5x}.$

Published on 15 Apr 2026 - 11:55

score 95 · Answer 13 · 2026-04-14 09:23:46

95

Views

Integral related to exponential function

Published on 14 Apr 2026 - 9:23

score 149 · Answer 14 · 2026-04-25 21:58:43

149

Views

How to prove the following ineqiulity : $\exp\left(\int_0^t f(s)ds \right) \le 1+ \int_0^t e^{\max(1,s)f(s)}ds$

Published on 25 Apr 2026 - 21:58

score 1.8k · Answer 15 · 2026-04-15 18:32:52

1.8k

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Show that if $\lim\limits_{x \to \infty} f(x)$ exists and $f''$ is bounded, then $\lim\limits_{x \to \infty} f'(x)=0$.

Published on 15 Apr 2026 - 18:32

List Question

Periodicity of $f$ such that $ f(x+2)=f(x-1)f(x+5)$

$X$ is the space of all continuous functions with the norm $||f||=\sup_{t\ge0}e^{kt}|f(t)|<\infty.$ Is $X$ a Banach space?

Integral inequality on decreasing function

Let $T \in L(\mathbb{R}^n,\mathbb{R}^m)$. Prove that $T$ is differentiable at every $x \in \mathbb{R}^n$.

Why the following constraint is non-convex? Is my explanation right or wrong?

Direct Relationship Between Second Derivative & Points of Inflection

If $f:[a,b]\to\mathbb{R}$ is a function of first class, does it mean that $f$ is continuous everywhere except countably many points in $[a,b]?$

Find all $f$ that satisfies $f:\mathbb{R}\rightarrow\mathbb{R};f(x+y)+f(x)f(y)=(1+x)f(y)+(1+y)f(x)+f(xy)$

Sequences unbounded above diverges?

How? Consider function $f : \mathbb {R} \rightarrow \mathbb {R}$ defined as $f (x)=x^2 + 3$. Find $f ([-3,5])$ and $f^{-1} ([12,19])$.

To prove an inequality of degree 3 polynomilals

Limits without L'Hopital $\lim\limits_{x\to 0} \frac{e^{3x}-e^{-4x}}{\sin5x}.$

Integral related to exponential function

How to prove the following ineqiulity : $\exp\left(\int_0^t f(s)ds \right) \le 1+ \int_0^t e^{\max(1,s)f(s)}ds$

Show that if $\lim\limits_{x \to \infty} f(x)$ exists and $f''$ is bounded, then $\lim\limits_{x \to \infty} f'(x)=0$.

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