This is pdfTeX, Version 3.14159265-2.6-1.40.21 (TeX Live 2020) (preloaded format=pdflatex 2020.12.16) 18 JAN 2022 04:45 entering extended mode restricted \write18 enabled. %&-line parsing enabled. **sln_final_mse21f.tex (./sln_final_mse21f.tex LaTeX2e <2020-10-01> patch level 2 L3 programming layer <2020-12-07> xparse <2020-03-03> (/usr/local/texlive/2020/texmf-dist/tex/latex/base/article.cls Document Class: article 2020/04/10 v1.4m Standard LaTeX document class (/usr/local/texlive/2020/texmf-dist/tex/latex/base/size12.clo File: size12.clo 2020/04/10 v1.4m Standard LaTeX file (size option) ) \c@part=\count177 \c@section=\count178 \c@subsection=\count179 \c@subsubsection=\count180 \c@paragraph=\count181 \c@subparagraph=\count182 \c@figure=\count183 \c@table=\count184 \abovecaptionskip=\skip47 \belowcaptionskip=\skip48 \bibindent=\dimen138 ) (/usr/local/texlive/2020/texmf-dist/tex/latex/amsmath/amsmath.sty Package: amsmath 2020/09/23 v2.17i AMS math features \@mathmargin=\skip49 For additional information on amsmath, use the `?' option. 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Overfull \hbox (14.31483pt too wide) in paragraph at lines 90--100 []\OT1/cmr/m/n/12 (12 pts) Find the so-lu-tions for (a): $[]\OML/cmm/m/it/12 ; y\OT1/cmr/m/n/12 (0) = 1\OML/cmm/m/it/12 ;$ \OT1/cmr/m/n/12 and (b): $[]\OML/c mm/m/it/12 ; y\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 ^^Y\OT1/cmr/m/n/12 ) = [] Overfull \hbox (17.0052pt too wide) detected at line 149 [] \OT1/cmr/m/n/12 : [][] \OML/cmm/m/it/12 x[]e[]dx [] \OT1/cmr/m/n/12 : [] [ ] : [] [] : [][] [][] \OML/cmm/m/it/12 x [][] x dx [] Overfull \hbox (34.51608pt too wide) detected at line 162 [] \OT1/cmr/m/n/12 : [][] [] \OML/cmm/m/it/12 dx [] \OT1/cmr/m/n/12 : [] [] : [] [] : [][] []\OML/cmm/m/it/12 dx [] [1 {/usr/local/texlive/2020/texmf-var/fonts/map/pdftex/updmap/pdftex.map}] Overfull \hbox (24.26114pt too wide) detected at line 180 \OT1/cmr/m/n/12 ([][] \OML/cmm/m/it/12 x\OT1/cmr/m/n/12 )[] = ([])[] = [] [][] 2\OML/cmm/m/it/12 x \OT1/cmr/m/n/12 + [] [] 2\OML/cmm/m/it/12 x \OT1/cmr/m/n/12 + [] = []([] 4\OML/cmm/m/it/12 x \OT1/cmr/m/n/12 + 1) + [] [] 2\OML/cmm/m/it/1 2 x \OT1/cmr/m/n/12 + [] [] Overfull \hbox (33.63602pt too wide) in alignment at lines 200--207 [][][] [] [] Overfull \hbox (54.11345pt too wide) detected at line 242 [] [] [2] Overfull \hbox (0.71043pt too wide) in paragraph at lines 277--281 []$[]$ \OT1/cmr/m/n/12 ($\U/msa/m/n/12 * [] \OML/cmm/m/it/12 x > [] [] x$ \OT1/ cmr/m/n/12 for $\OML/cmm/m/it/12 x$ \OT1/cmr/m/n/12 large enough). [] [3] [4] (./sln_final_mse21f.aux) ) Here is how much of TeX's memory you used: 2371 strings out of 479383 31533 string characters out of 5869372 323875 words of memory out of 5000000 19484 multiletter control sequences out of 15000+600000 408680 words of font info for 47 fonts, out of 8000000 for 9000 1141 hyphenation exceptions out of 8191 66i,13n,72p,233b,275s stack positions out of 5000i,500n,10000p,200000b,80000s Output written on sln_final_mse21f.pdf (4 pages, 118587 bytes). PDF statistics: 61 PDF objects out of 1000 (max. 8388607) 43 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) ns out of 1000 (max. 500000) 1 words of extra memory for PDF output out of 10000 (max. 10000000)