Question

If $|f(z)-w|<|w|/2$ how do you conclude $|f(z)|>|w|/2$? $z$ and non-zero $w$ are complex numbers.

score 46 · Answer 1 · 2026-04-02 13:26:57

46

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If $|f(z)-w|<|w|/2$ how do you conclude $|f(z)|>|w|/2$? $z$ and non-zero $w$ are complex numbers.

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score 118 · Answer 2 · 2026-03-26 08:14:37

118

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score 1.5k · Answer 3 · 2026-04-09 08:43:59

1.5k

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score 81 · Answer 4 · 2026-03-27 17:06:02

81

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Find exhaustive range of $k$ such that $f(x)=\frac{x-1}{k-x^2}$ never belongs to $\left[-1 \:\: \frac{-1}{3}\right]$

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score 144 · Answer 5 · 2026-03-26 06:34:30

144

Views

Maximise $(x+1)\sqrt{1-x^2}$ without calculus

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score 140 · Answer 6 · 2026-03-27 17:04:22

140

Views

Why this $12b^2<49ac< \frac{49}{4}b^2$ inequality given ? What is the use of it?

Published on 27 Mar 2026 - 17:04

score 93 · Answer 7 · 2026-03-25 15:57:09

93

Views

Find maximum value

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score 256 · Answer 8 · 2026-03-25 22:25:14

256

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score 100 · Answer 9 · 2018-10-18 08:56:03

100

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Proof of $ n! \lt \Big(\frac{n+1}{2}\Big)^n$

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score 45 · Answer 10 · 2026-03-27 09:15:01

45

Views

How to bound $(\frac{a}{x}+\frac{b}{y})(x+y)$ for large $x,y$ and positive $a,b$

Published on 27 Mar 2026 - 9:15

score 73 · Answer 11 · 2026-03-25 22:30:55

73

Views

Is it allowed to solve this inequality $x|x-1|>-3$ by dividing each member with $x$?

Published on 25 Mar 2026 - 22:30

score 112 · Answer 12 · 2026-03-24 20:32:02

112

Views

$4ac-b^2\leq 3a(a+b+c)$ in quadratic

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score 2.2k · Answer 13 · 2026-03-26 03:10:57

2.2k

Views

Prove function in two variables is convex

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score 1.2k · Answer 14 · 2026-03-26 17:50:22

1.2k

Views

If $0<x<y$, then prove that $\sqrt{x} <\sqrt{y}$ and $x <\sqrt{xy} <y$

Published on 26 Mar 2026 - 17:50

score 45 · Answer 15 · 2018-10-19 05:05:03

45

Views

Show that $\sum_{n=1}^{2^k-1} 1/n^p < \sum_{n=0}^{k-1} (1/2^ { p-1})^n)$

Published on 19 Oct 2018 - 5:05

List Question

If $|f(z)-w|<|w|/2$ how do you conclude $|f(z)|>|w|/2$? $z$ and non-zero $w$ are complex numbers.

Inequality for contests

Minkowski inequality proof without using Holder's inequality

Find exhaustive range of $k$ such that $f(x)=\frac{x-1}{k-x^2}$ never belongs to $\left[-1 \:\: \frac{-1}{3}\right]$

Maximise $(x+1)\sqrt{1-x^2}$ without calculus

Why this $12b^2<49ac< \frac{49}{4}b^2$ inequality given ? What is the use of it?

Find maximum value

Square root of absolute difference is greater than absolute of square root difference

Proof of $ n! \lt \Big(\frac{n+1}{2}\Big)^n$

How to bound $(\frac{a}{x}+\frac{b}{y})(x+y)$ for large $x,y$ and positive $a,b$

Is it allowed to solve this inequality $x|x-1|>-3$ by dividing each member with $x$?

$4ac-b^2\leq 3a(a+b+c)$ in quadratic

Prove function in two variables is convex

If $0<x<y$, then prove that $\sqrt{x} <\sqrt{y}$ and $x <\sqrt{xy} <y$

Show that $\sum_{n=1}^{2^k-1} 1/n^p < \sum_{n=0}^{k-1} (1/2^ { p-1})^n)$

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