This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015) (preloaded format=pdftex 2016.1.11) 20 SEP 2020 10:12 entering extended mode restricted \write18 enabled. %&-line parsing enabled. **ho144 (./ho144.tex Overfull \hbox (1.66286pt too wide) detected at line 67 \teni f[] \tenrm = [](9\teni x[] \tenrm + \teni y[] \tenrm + 6\teni x \tensy ^^ @ \tenrm 3\teni y \tenrm + 5) = 18\teni x \tenrm + 6 \teni ; \hbox(13.70952+6.85951)x180.0, glue set - 1.0 .\teni f .\hbox(3.01389+0.0)x5.03473, shifted 1.49998 ..\seveni x .\glue(\thickmuskip) 2.77771 plus 2.77771 .\tenrm = .\glue(\thickmuskip) 2.77771 plus 2.77771 .etc. Overfull \hbox (20.83029pt too wide) detected at line 93 \teni z \tensy ^^@ \teni z[] \tenrm = \teni f[]\tenrm (\teni x[]; y[]\tenrm )(\ teni x \tensy ^^@ \teni x[]\tenrm ) + \teni f[]\tenrm (\teni x[]; y[]\tenrm )(\ teni y \tensy ^^@ \teni y[]\tenrm ) \teni : \hbox(7.5+2.86108)x180.0, glue set - 1.0 .\teni z .\kern0.4398 .\glue(\medmuskip) 2.22217 plus 1.11108 minus 2.22217 .\tensy ^^@ .\glue(\medmuskip) 2.22217 plus 1.11108 minus 2.22217 .etc. Overfull \hbox (6.42514pt too wide) in paragraph at lines 93--96 \tenrm prob-lem and $\teni f[]\tenrm (\teni x[]; y[]\tenrm )\teni ; f[]\tenrm ( \teni x[]; y[]\tenrm )$ from step \hbox(7.5+2.86108)x180.0, glue set - 1.0 .\tenrm p .\tenrm r .\tenrm o .\tenrm b .\discretionary ..\tenrm - .etc. [1{/usr/local/texlive/2015/texmf-var/fonts/map/pdftex/updmap/pdftex.map}] Overfull \hbox (49.04024pt too wide) detected at line 131 \teni f[] \tenrm = []\teni e[] []\tenrm (\teni xy\tenrm ) = ([]\teni e[]\tenrm ) [](\teni xy\tenrm ) + \teni e[]\tenrm ([] [](\teni xy\tenrm )) \hbox(13.70952+6.85951)x180.0, glue set - 1.0 .\teni f .\hbox(3.01389+0.0)x5.03473, shifted 1.49998 ..\seveni x .\glue(\thickmuskip) 2.77771 plus 2.77771 .\tenrm = .\glue(\thickmuskip) 2.77771 plus 2.77771 .etc. Overfull \hbox (51.30685pt too wide) detected at line 140 \teni f[] \tenrm = []\teni e[] []\tenrm (\teni xy\tenrm ) = \teni e[]\tenrm ([] [](\teni xy\tenrm )) = \teni e[]x []\tenrm (\teni xy\tenrm ) \teni : \hbox(13.70952+8.80396)x180.0 .\teni f .\hbox(3.01389+1.3611)x4.80675, shifted 1.49998 ..\seveni y .\glue(\thickmuskip) 2.77771 plus 2.77771 .\tenrm = .\glue(\thickmuskip) 2.77771 plus 2.77771 .etc. Overfull \hbox (8.46672pt too wide) in paragraph at lines 156--162 \teni e[]x []\tenrm (\teni xy\tenrm )$ are both con-tin-u-ous at the point \hbox(7.5+2.5)x180.0, glue set - 1.0 .\teni e .\hbox(3.01389+0.0)x5.03473, shifted -3.62892 ..\seveni x .\teni x .\glue(\thinmuskip) 1.66663 .\hbox(4.30554+0.0)x13.3889 ..\tenrm c ..\tenrm o ..\tenrm s .etc. Overfull \hbox (25.94807pt too wide) detected at line 167 \teni f[]\tenrm (0\teni ; ^^Y=\tenrm 2) = \teni e[] []\tenrm (0) + \teni e[] \t ensy ^^A \tenrm (\teni ^^Y=\tenrm 2) [](0) = \teni ^^Y=\tenrm 2 \teni ; \hbox(8.64003+2.5)x180.0, glue set - 1.0 .\teni f .\hbox(3.01389+0.0)x5.03473, shifted 1.49998 ..\seveni x .\tenrm ( .\tenrm 0 .\teni ; .etc. Overfull \hbox (37.09631pt too wide) detected at line 175 \teni L\tenrm (\teni x; y\tenrm ) = 0 + (\teni ^^Y=\tenrm 2) \tensy ^^A \tenrm (\teni x \tensy ^^@ \tenrm 0) + 0 \tensy ^^A \tenrm (\teni y \tensy ^^@ \teni ^ ^Y=\tenrm 2) = (\teni ^^Y=\tenrm 2)\teni x : \hbox(7.5+2.5)x180.0, glue set - 1.0 .\teni L .\tenrm ( .\teni x .\teni ; .\glue(\thinmuskip) 1.66663 .etc. [2] Overfull \hbox (70.35754pt too wide) detected at line 213 \teni f[] \tenrm = [](20 \tensy ^^@ \teni x[] \tensy ^^@ \tenrm 2\teni y[]\tenr m )[] = (1\teni =\tenrm 2)(20 \tensy ^^@ \teni x[] \tensy ^^@ \tenrm 2\teni y[] \tenrm )[] \tensy ^^A \tenrm (\tensy ^^@\tenrm 2\teni x\tenrm ) \hbox(13.70952+6.85951)x180.0, glue set - 1.0 .\teni f .\hbox(3.01389+0.0)x5.03473, shifted 1.49998 ..\seveni x .\glue(\thickmuskip) 2.77771 plus 2.77771 .\tenrm = .\glue(\thickmuskip) 2.77771 plus 2.77771 .etc. Overfull \hbox (69.22221pt too wide) detected at line 220 \teni f[] \tenrm = [](20 \tensy ^^@ \teni x[] \tensy ^^@ \tenrm 2\teni y[]\tenr m )[] = (1\teni =\tenrm 2)(20 \tensy ^^@ \teni x[] \tensy ^^@ \tenrm 2\teni y[] \tenrm )[] \tensy ^^A \tenrm (\tensy ^^@\tenrm 4\teni y\tenrm ) \hbox(13.70952+8.80396)x180.0, glue set - 1.0 .\teni f .\hbox(3.01389+1.3611)x4.80675, shifted 1.49998 ..\seveni y .\glue(\thickmuskip) 2.77771 plus 2.77771 .\tenrm = .\glue(\thickmuskip) 2.77771 plus 2.77771 .etc. Overfull \hbox (34.34163pt too wide) detected at line 233 \teni L\tenrm (\teni x; y\tenrm ) = \teni f\tenrm (\teni a; b\tenrm ) + \teni f []\tenrm (\teni a; b\tenrm )(\teni x \tensy ^^@ \teni a\tenrm ) + \teni f[]\ten rm (\teni a; b\tenrm )(\teni y \tensy ^^@ \teni b\tenrm ) \teni : \hbox(7.5+2.86108)x180.0, glue set - 1.0 .\teni L .\tenrm ( .\teni x .\teni ; .\glue(\thinmuskip) 1.66663 .etc. Overfull \hbox (3.55153pt too wide) in paragraph at lines 235--240 \tenbf 2. $\teni f[] \tenrm = []$ and $\teni f[] \tenrm = []$ \hbox(8.97218+8.49994)x180.0, glue set - 1.0 .\tenbf 2 .\tenbf . .\glue 4.44444 plus 4.99997 minus 0.37036 .\mathon .\teni f .etc. Overfull \hbox (3.25029pt too wide) in paragraph at lines 235--240 \tenrm (the ar-gu-ment of the square-root is $9$ which \hbox(7.5+2.5)x180.0, glue set - 1.0 .\tenrm ( .\tenrm t .\tenrm h .\tenrm e .\glue 3.33333 plus 1.66666 minus 1.11111 .etc. Overfull \hbox (2.86052pt too wide) in paragraph at lines 252--254 \tenrm So the \tenbf lin-ear ap-prox-i-ma-tion\tenrm , valid \tenbf near \hbox(6.94444+1.94444)x180.0, glue set - 1.0 .\tenrm S .\tenrm o .\glue 3.33333 plus 1.66666 minus 1.11111 .\tenrm t .\tenrm h .etc. Overfull \hbox (10.41699pt too wide) detected at line 266 \teni f\tenrm (3\teni :\tenrm 05\teni ; :\tenrm 97) \tensy ^^Y \tenrm 3 \tensy ^^@ \tenrm (3\teni :\tenrm 05 \tensy ^^@ \tenrm 3) \tensy ^^@ \tenrm (2\teni =\ tenrm 3) \tensy ^^A \tenrm (\teni :\tenrm 97 \tensy ^^@ \tenrm 1) = \hbox(7.5+2.5)x180.0, glue set - 1.0 .\teni f .\kern1.0764 .\tenrm ( .\tenrm 3 .\teni : .etc. Underfull \vbox (badness 10000) has occurred while \output is active \vbox(587.39885+4.0)x428.99947, glue set 34.77724 .\glue(\topskip) 2.5 .\hbox(7.5+2.5)x428.99947, glue set - 0.34145 ..\hbox(0.0+0.0)x0.0 ..\tenbf P ..\tenbf r ..\tenbf o ..\tenbf b ..etc. .\penalty 300 .\glue(\baselineskip) 4.0 .\hbox(7.5+2.5)x428.99947, glue set 256.23888fil ..\teni f ..\kern1.0764 ..\tenrm ( ..\teni a ..\hbox(4.51111+0.0)x4.48613, shifted 1.49998 ...\sevenrm 1 ..etc. .etc. [3] [4] ) Output written on ho144.pdf (4 pages, 113593 bytes). PDF statistics: 57 PDF objects out of 1000 (max. 8388607) 40 compressed objects within 1 object stream 0 named destinations out of 1000 (max. 500000) 1 words of extra memory for PDF output out of 10000 (max. 10000000)