       RE: For a variety of plotting experiences, maybe bugs? (small intervals)

• To: mathgroup at smc.vnet.net
• Subject: [mg124114] RE: [mg124074] For a variety of plotting experiences, maybe bugs? (small intervals)
• From: "David Park" <djmpark at comcast.net>
• Date: Mon, 9 Jan 2012 03:20:17 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <je3vti\$eeh\$1@smc.vnet.net> <je6e5h\$q7b\$1@smc.vnet.net> <24475751.93762.1326015447306.JavaMail.root@m06>

```Small domains and small intervals are often treated masochistically. And why
the powers of 2 instead of 10?

This is the easy way to make the plots. Use a reasonable domain and range
and enough WorkingPrecision.

With[{n = 140},
Plot[(Cos[x 10^-n + 1] - Cos) 10^n, {x, 0, 1},
WorkingPrecision -> n + 3,
Frame -> True,
FrameLabel -> {(y - 1) 10.^n, 10.^n (Cos[y] - Cos)}]
]

Or use a series expansion:

Series[10^n (Cos[1 + x 10^-n] - Cos), {x, 0, 2}] // Normal

-2^(-1 - n) 5^-n x^2 Cos - x Sin

and then use MachinePrecision:

With[{n = 145},
Plot[-2^(-1 - n) 5^-n x^2 Cos - x Sin, {x, 0, 1},
WorkingPrecision -> MachinePrecision,
Frame -> True,
FrameLabel -> {(y - 1) 10.^n, 10.^n (Cos[y] - Cos)}]
]

That is the way they do it in technical journals all the time.

David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/index.html

From: Richard Fateman [mailto:fateman at cs.berkeley.edu]

try this (I did it on version 7...)
>

Table[Plot[Cos[x], {x, 1 , 1 + 2.0^-i}], {i, 40, 45}]

```

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