{{{id=1| b=RR(3.0, 1000) places=6 left = [[N(-10^-k,digits=places),N((b^(-(10^-k)) - 1)/(-(10^-k)), digits=places)] for k in range(1,places+1,1)] right = [[N(10^-k,digits=places),N((b^(10^-k) - 1)/(10^-k), digits=places)] for k in range(places,0,-1)] html.table([['$h$','$(b^h-1)/h$']] + left + [[0,'undefined']] + right) ///

$h$	$(b^h-1)/h$
$-0.100000$	$1.04042$
$-0.0100000$	$1.09260$
$-0.00100000$	$1.09801$
$-0.000100000$	$1.09855$
$-0.0000100000$	$1.09861$
$-1.00000 \times 10^{-6}$	$1.09861$
$0$	undefined
$1.00000 \times 10^{-6}$	$1.09861$
$0.0000100000$	$1.09862$
$0.000100000$	$1.09867$
$0.00100000$	$1.09922$
$0.0100000$	$1.10467$
$0.100000$	$1.16123$

}}} {{{id=4| /// }}} {{{id=2| html.table(left+right) ///

$0.10000000000000000000$	$0.71773462536293164212$
$0.010000000000000000000$	$0.69555500567188088324$
$0.0010000000000000000000$	$0.69338746258063253813$
$0.00010000000000000000000$	$0.69317120376569191231$
$0.000010000000000000000000$	$0.69314958283056526955$
$1.0000000000000000000 \times 10^{-6}$	$0.69314742078650759538$
$1.0000000000000000000 \times 10^{-7}$	$0.69314720458260126179$
$1.0000000000000000000 \times 10^{-8}$	$0.69314718296220689808$
$1.0000000000000000000 \times 10^{-9}$	$0.69314718079931481043$
$1.0000000000000000000 \times 10^{-10}$	$0.69314718058740254492$
$1.0000000000000000000 \times 10^{-11}$	$0.69314718048553913832$
$1.0000000000000000000 \times 10^{-12}$	$0.69314718153327703476$
$1.0000000000000000000 \times 10^{-13}$	$0.69314718246459960938$
$1.0000000000000000000 \times 10^{-14}$	$0.69314718246459960938$
$1.0000000000000000000 \times 10^{-15}$	$0.69314765930175781250$
$1.0000000000000000000 \times 10^{-16}$	$0.69314575195312500000$
$1.0000000000000000000 \times 10^{-17}$	$0.69323730468750000000$
$1.0000000000000000000 \times 10^{-18}$	$0.69335937500000000000$
$1.0000000000000000000 \times 10^{-19}$	$0.68750000000000000000$
$-1.0000000000000000000 \times 10^{-20}$	$0.62500000000000000000$
$-1.0000000000000000000 \times 10^{-19}$	$0.68750000000000000000$
$-1.0000000000000000000 \times 10^{-18}$	$0.69335937500000000000$
$-1.0000000000000000000 \times 10^{-17}$	$0.69311523437500000000$
$-1.0000000000000000000 \times 10^{-16}$	$0.69314575195312500000$
$-1.0000000000000000000 \times 10^{-15}$	$0.69314765930175781250$
$-1.0000000000000000000 \times 10^{-14}$	$0.69314718246459960938$
$-1.0000000000000000000 \times 10^{-13}$	$0.69314718246459960938$
$-1.0000000000000000000 \times 10^{-12}$	$0.69314718060195446014$
$-1.0000000000000000000 \times 10^{-11}$	$0.69314718060195446014$
$-1.0000000000000000000 \times 10^{-10}$	$0.69314718054374679923$
$-1.0000000000000000000 \times 10^{-9}$	$0.69314718031910160789$
$-1.0000000000000000000 \times 10^{-8}$	$0.69314717815768744913$
$-1.0000000000000000000 \times 10^{-7}$	$0.69314715653729308542$
$-1.0000000000000000000 \times 10^{-6}$	$0.69314694033349333324$
$-0.000010000000000000000000$	$0.69314477830042608986$
$-0.00010000000000000000000$	$0.69312315846428086685$
$-0.0010000000000000000000$	$0.69290700954747807758$
$-0.010000000000000000000$	$0.69075045629640984674$

}}} {{{id=3| /// }}}