Nicole Torcolini
October 8, 2006

Nemetex Nemeth Back-Translator Demonstration Document

#1_4 #14.90+5.10 .k #20

#2_4 #1-.8511 .k #.1489

#3_4 #412`*.58 .k #238.96

#4_4 ?1/6# .k #0.1666:

#5_4 #0 "k x "k #10
#0 "k: y "k: #10

#6_4 -?.p/4# "k .? "k ?.p/2#

#7_4 ,??w/x#,/?y/z#,#

#8_4 ?1/>2}#`*?2/>6}# .k ?>2}/2#`*?2>6}/6# .k ?2>2}>6}/12# .k ?2>12}/12# .k ?>12}/6# .k ?2>3}/6# .k ?>3}/3# `:`: #0.577

#9_4 ?x~2"/4#-?y~2"/16# .k #1

#10_4 #5~6"`*2~4"`*3~5 .k #60,750,000

#11_4 #5& .k #120

#12_4 #5~25x~~30~+2"+1

#13_4 $t ,a,b,c `:.k $t ,d,e,f

#14_4 a .k .(#2 #4 #6 #8.)
b .k .(#3 #6 #9 #12.)
a.+b .k .(#2 #3 #4 #6 #8 #9 #10 #12.)
a.%b .k .(#6.)

#15_4 ",a,b<${33o} $p ",c,d<${33o}

#16_4 <4>a~5"b} .k a~5_/4"b~1_/4

#17_4 #64x~3"+240x~2"y+300xy~2"+125y~3

#18_4 f~-1"(x) .k log;x (?3/4#)

#19_4 #73./tan #75~.* `:`: #20 inches

#20_4 ln x-ln 2 .k #4ln y

#21_4 ,?5-?1/x~3"#,/?4/x~3"#-2,# .k ,?(5-?1/x~2"#)x~3",/(?4/x~3"-2#)x~3",# .k ?5x~3"-1/4-2x~3"#, x /.k <3>2}, x /.k #0

#22_4 arctan (?3/6#) .k arctan (?1/2#) `:`: #26.6~.*

#23_4 arccos(-?13~2"-(12~2"+5~2")/2`*12`*5#) .k #90~.*

#24_4 sin #90~.* .k #1

#25_4 e~-2.58 `:`: #0.075774

#26_4
#5x~2"+2x+7 .k #4x+11
#5x~2"+2x-4x+7-11 .k #4x-4x+11-11
#5x~2"-2x-4 .k #0

#27_4 p $77o q _l `:q $77o `:p

#28_4 p $77o q
`:q
,* `:p

#29_4 ;a_4 "lim%x $o #0~+"} ?5/x~4"# .k ,=, "lim%x $o #0~-"} ?5/x~4"# $o ,=
;b_4 "lim%x $o ,=} ?5/x~4"# .k #0, "lim%x $o -,=} ?5/x~4"# .k #0

#30_4 f(x1+.,dx)

#31_4 ".,s%i .k #1<k}i .k ?k(k+1)/2#

#32_4 (5%3) .k ?5&/3&(5-3)&# .k ?5&/6`*2&# .k ?120/6`*2# .k ?120/12# .k #10

#33_4 ;a_4 There is a largest degree for a polynomial.
;b_4 The degree of a polynomial is any nonnegative integer.  Suppose there exists a largest integer degree n for a polynomial.  Then, because the integers are closed under addition, n+1 is also an integer and a possible degree.  Because n+1 .1 n, n is not the largest possible degree for a polynomial.  Therefore there is no largest degree for a polynomial.

#34_4 `,(a b c`,)`*`,(g h`,) .k `,(ag+bi+ck ah+bj+cl`,)
     `,(d e f`,)  `,(i j`,)    `,(dg+ei+fk dh+ej+fl`,)
                  `,(k l`,)

#35_4 !;a~b"2x~3"dx