Question

Prove Newton's iteration will diverge for these functions, no matter what real starting point is selected. $f(x)=x^2+1$ and $g(x)=7x^4+3x^2+\pi$.

score 3.4k · Answer 1 · 2026-04-14 16:16:47

3.4k

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Prove Newton's iteration will diverge for these functions, no matter what real starting point is selected. $f(x)=x^2+1$ and $g(x)=7x^4+3x^2+\pi$.

Published on 14 Apr 2026 - 16:16

score 147 · Answer 2 · 2026-04-11 06:04:57

147

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Difficult applications of Rouche's Theorem to tangent and exp functions

Published on 11 Apr 2026 - 6:04

score 420 · Answer 3 · 2026-04-20 05:57:41

420

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Muliplicty of the roots of the graph (x^4)-2

Published on 20 Apr 2026 - 5:57

score 370 · Answer 4 · 2026-04-15 15:51:23

370

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Zeros of real analytic functions

Published on 15 Apr 2026 - 15:51

score 201 · Answer 5 · 2026-04-20 11:59:09

201

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$Z^4 = -1$ How do I solve this without a calculator?

Published on 20 Apr 2026 - 11:59

score 367 · Answer 6 · 2026-04-20 12:22:30

367

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11 combinations of quintic functions

Published on 20 Apr 2026 - 12:22

score 100 · Answer 7 · 2026-04-04 03:45:04

100

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Does a function with an exponential growth condition necessarily have infinitely many zeros?

Published on 04 Apr 2026 - 3:45

score 279 · Answer 8 · 2026-03-29 06:06:16

279

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Roots of a polynomial that is composed n times with itself

Published on 29 Mar 2026 - 6:06

score 333 · Answer 9 · 2026-04-15 20:46:49

333

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What is the fastest technique to find complex roots of a function?

Published on 15 Apr 2026 - 20:46

score 66 · Answer 10 · 2026-04-20 07:12:44

66

Views

Prove that $z^5+(4/3)e^z \sin z-16iz+48$ has five zeroes in the disk $|z|<3$

Published on 20 Apr 2026 - 7:12

score 149 · Answer 11 · 2026-04-06 01:13:58

149

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find the solution set of the following equation with absolute value

Published on 06 Apr 2026 - 1:13

score 193 · Answer 12 · 2026-04-08 02:35:34

193

Views

Symmetric proof for the probability of real roots of a quadratic with exponentially distributed parameters

Published on 08 Apr 2026 - 2:35

score 1.5k · Answer 13 · 2026-04-20 12:22:18

1.5k

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oscillation of newton iteration for arctan

Published on 20 Apr 2026 - 12:22

score 144 · Answer 14 · 2026-04-20 12:29:33

144

Views

How to solve $e^x=kx + 1$ when $k > 1$?

Published on 20 Apr 2026 - 12:29

score 57 · Answer 15 · 2015-10-14 17:15:06

57

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Nulls are located at all primes on the real axis?

Published on 14 Oct 2015 - 17:15

List Question

Prove Newton's iteration will diverge for these functions, no matter what real starting point is selected. $f(x)=x^2+1$ and $g(x)=7x^4+3x^2+\pi$.

Difficult applications of Rouche's Theorem to tangent and exp functions

Muliplicty of the roots of the graph (x^4)-2

Zeros of real analytic functions

$Z^4 = -1$ How do I solve this without a calculator?

11 combinations of quintic functions

Does a function with an exponential growth condition necessarily have infinitely many zeros?

Roots of a polynomial that is composed n times with itself

What is the fastest technique to find complex roots of a function?

Prove that $z^5+(4/3)e^z \sin z-16iz+48$ has five zeroes in the disk $|z|<3$

find the solution set of the following equation with absolute value

Symmetric proof for the probability of real roots of a quadratic with exponentially distributed parameters

oscillation of newton iteration for arctan

How to solve $e^x=kx + 1$ when $k > 1$?

Nulls are located at all primes on the real axis?

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