{"id":6695,"date":"2021-07-20T23:57:46","date_gmt":"2021-07-20T14:57:46","guid":{"rendered":"https:\/\/sasamath.com\/blog\/?page_id=6695"},"modified":"2022-03-06T19:51:35","modified_gmt":"2022-03-06T10:51:35","slug":"one-sided-limits","status":"publish","type":"page","link":"https:\/\/sasamath.com\/blog\/invitation-to-calculus\/one-sided-limits\/","title":{"rendered":"\uc88c\uadf9\ud55c\uacfc \uc6b0\uadf9\ud55c"},"content":{"rendered":"<div style=\"display: none; visibility: hidden;\">\n<style type=\"text\/css\">\n\timg.mfp-img { background-color: white; }\n<\/style>\n<p><!--\n\\[\n\\newcommand{\\vecf}{{\\mathbf{f}}}\n\\newcommand{\\vecL}{{\\mathbf{L}}}\n\\newcommand{\\vecR}{{\\mathbb{R}}}\n\\newcommand{\\imI}{\\boldsymbol{i}}\n\\]\n-->\n<\/div>\n<div class=\"box itc_intro\">\n<p>\uc774 \uae00\uc740 \u300e\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c\u300f 3\uc7a5 3\uc808\uc758 \ub0b4\uc6a9\uc785\ub2c8\ub2e4.&nbsp; <span class=\"itc_viewcontents\">(<a href=\"..\/\">\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c \ucc28\ub840 \ubcf4\uae30<\/a>)<\/span><\/p>\n<\/div>\n<p>\uc810 \\(c\\)\uc5d0\uc11c \ud568\uc218 \\(f\\)\uc758 \uadf9\ud55c\uc744 \uc0dd\uac01\ud560 \ub54c, \\(x\\)\uac00 \\(c\\)\uc758 \uc67c\ucabd\uc73c\ub85c\ubd80\ud130 \\(c\\)\uc5d0 \ub2e4\uac00\uac00\ub294 \uacbd\uc6b0\uc640 \\(x\\)\uac00 \\(c\\)\uc758 \uc624\ub978\ucabd\uc73c\ub85c\ubd80\ud130 \\(c\\)\uc5d0 \ub2e4\uac00\uac00\ub294 \uacbd\uc6b0\ub97c \uc0dd\uac01\ud560 \uc218 \uc788\ub2e4.<\/p>\n<p>\\(f:D \\rightarrow \\mathbb{R}\\)\uac00 \ud568\uc218\uc774\uace0 \\(c\\)\uac00 \\(D\\)\uc758 \uc810\uc774\ub77c\uace0 \ud558\uc790.<\/p>\n<div class=\"margintop2 marginbottom2\">\n<img decoding=\"async\" src=\"\/blog\/wp-content\/uploads\/2021\/08\/ic_ch03_se03_img01.png\" alt=\"\" width=\"187\" height=\"182\" class=\"aligncenter size-full wp-image-7255\" srcset=\"https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/ic_ch03_se03_img01.png 562w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/ic_ch03_se03_img01-300x291.png 300w\" sizes=\"(max-width: 187px) 100vw, 187px\" \/>\n<\/div>\n<p>\ub9cc\uc57d \\(x\\)\uac00 \\(x < c\\)\ub97c \uc720\uc9c0\ud55c \ucc44\ub85c \\(c\\)\uc5d0 \ub2e4\uac00\uac08 \ub54c \\(f(x)\\)\uac00 \ud558\ub098\uc758 \uac12 \\(L\\)\uc5d0 \ub2e4\uac00\uac00\uba74, \\(L\\)\uc744 \\(c\\)\uc5d0\uc11c \\(f(x)\\)\uc758 <span class=\"defined\">\uc88c\uadf9\ud55c<\/span>(left-sided limit)\uc774\ub77c\uace0 \ubd80\ub974\uace0, \uc774 \uc0c1\ud669\uc744 \uae30\ud638\ub85c<br \/>\n\\[\\lim_{x\\rightarrow c^-} f(x) =L\\]<br \/>\n\ub610\ub294<br \/>\n\\[f(x) \\rightarrow L \\quad \\text{as} \\quad x \\rightarrow c^-\\]<br \/>\n\uc640 \uac19\uc774 \ub098\ud0c0\ub0b8\ub2e4.<\/p>\n<p>\ub9cc\uc57d \\(x\\)\uac00 \\(c < x\\)\ub97c \uc720\uc9c0\ud55c \ucc44\ub85c \\(c\\)\uc5d0 \ub2e4\uac00\uac08 \ub54c \\(f(x)\\)\uac00 \ud558\ub098\uc758 \uac12 \\(M\\)\uc5d0 \ub2e4\uac00\uac00\uba74, \\(M\\)\uc744 \\(c\\)\uc5d0\uc11c \\(f(x)\\)\uc758 <span class=\"defined\">\uc6b0\uadf9\ud55c<\/span>(right-sided limit)\uc774\ub77c\uace0 \ubd80\ub974\uace0, \uc774 \uc0c1\ud669\uc744 \uae30\ud638\ub85c<br \/>\n\\[\\lim_{x\\rightarrow c^+} f(x) = M\\]<br \/>\n\ub610\ub294<br \/>\n\\[f(x) \\rightarrow M \\quad \\text{as} \\quad x \\rightarrow c^+\\]<br \/>\n\uc640 \uac19\uc774 \ub098\ud0c0\ub0b8\ub2e4.<\/p>\n<p>\uc88c\uadf9\ud55c\uacfc \uc6b0\uadf9\ud55c\uc744 \ud1b5\ud2c0\uc5b4 <span class=\"defined\">\ud55c \ubc29\ud5a5 \uadf9\ud55c<\/span>(one-sided limits)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.<\/p>\n<p>\\(c\\)\uc5d0\uc11c \\(f:D\\rightarrow \\mathbb{R}\\)\uc758 \uc88c\uadf9\ud55c\uc774 \uc815\uc758\ub418\ub824\uba74 \\(x\\)\uac00 \\(D\\)\uc5d0 \uc18d\ud558\uba74\uc11c \\(c\\)\uc758 \uc67c\ucabd\uc5d0\uc11c \ub2e4\uac00\uac08 \uc218 \uc788\uc5b4\uc57c \ud55c\ub2e4. \uc989 \\(c\\)\uac00 \\((-\\infty ,\\, c) \\cap D\\)\uc758 \uc9d1\uc801\uc810\uc774\uc5b4\uc57c \ud55c\ub2e4. \ub9c8\ucc2c\uac00\uc9c0\ub85c \\(c\\)\uc5d0\uc11c \\(f\\)\uc758 \uc6b0\uadf9\ud55c\uc774 \uc815\uc758\ub418\ub824\uba74 \\(c\\)\uac00 \\((c,\\,\\infty ) \\cap D\\)\uc758 \uc9d1\uc801\uc810\uc774\uc5b4\uc57c \ud55c\ub2e4.<\/p>\n<p><p>\ud55c \ubc29\ud5a5 \uadf9\ud55c\uc774 \ubc1c\uc0b0\ud558\ub294 \uacbd\uc6b0\ub3c4 \uc218\ub834\ud558\ub294 \uacbd\uc6b0\uc640 \ub9c8\ucc2c\uac00\uc9c0 \ubc29\ubc95\uc73c\ub85c \uc815\uc758\ud55c\ub2e4.<\/p>\n<div class=\"example\">\n<p><span class=\"example\">\ubcf4\uae30 3.1.1.<\/span><\/p>\n<ol class=\"parenthesis\">\n<li>\\(f(x) = \\lfloor x \\rfloor\\)\uc774\uace0 \\(n\\)\uc774 \uc815\uc218\ub77c\uace0 \ud558\uc790. \uadf8\ub7ec\uba74<br \/>\n\\[\\lim_{x\\rightarrow n^-} f(x) = n-1 \\quad\\text{and}\\quad \\lim_{x\\rightarrow n^+} f(x)=n\\]<br \/>\n\uc774\ub2e4. \ub9cc\uc57d \\(c\\)\uac00 \uc815\uc218\uac00 \uc544\ub2cc \uc2e4\uc218\ub77c\uba74<br \/>\n\\[\\lim_{x\\rightarrow c^-} f(x) = \\lim_{x\\rightarrow c^+} f(x) = f(c)\\]<br \/>\n\uc774\ub2e4.<\/li>\n<div class=\"marginbottom2\">\n<img decoding=\"async\" src=\"\/blog\/wp-content\/uploads\/2021\/08\/ic_ch03_se03_img02.png\" alt=\"\" width=\"172\" height=\"164\" class=\"aligncenter size-full wp-image-7256\" srcset=\"https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/ic_ch03_se03_img02.png 516w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/08\/ic_ch03_se03_img02-300x285.png 300w\" sizes=\"(max-width: 172px) 100vw, 172px\" \/>\n<\/div>\n<li>\\(f(x) = \\frac{1}{x}\\)\uc774\uba74<br \/>\n\\[\\lim_{x\\rightarrow 0^-} f(x) = -\\infty \\quad\\text{and}\\quad \\lim_{x\\rightarrow 0^+} f(x) = \\infty\\]<br \/>\n\uc774\ub2e4.<\/li>\n<li>\\(p\\)\uac00 \ub2e4\ud56d\ud568\uc218\uc774\uace0 \\(c\\)\uac00 \uc2e4\uc218\uc774\uba74<br \/>\n\\[\\lim_{x\\rightarrow c^-} p(x) = p(c) \\quad\\text{and}\\quad \\lim_{x\\rightarrow c^+} p(x) = p(c)\\]<br \/>\n\uc774\ub2e4.<\/li>\n<li>\\(f(x) = \\frac{\\sin x}{x}\\)\uc774\uba74<br \/>\n\\[\\lim_{x\\rightarrow 0^-} f(x) = \\infty \\quad\\text{and}\\quad \\lim_{x\\rightarrow 0^+} f(x) = \\infty\\]<br \/>\n\uc774\ub2e4.<\/li>\n<li>\\(f(x) = \\sin \\frac{1}{x}\\)\uc774\uba74 \\(0\\)\uc5d0\uc11c \\(f\\)\uc758 \uc88c\uadf9\ud55c\uacfc \uc6b0\uadf9\ud55c\uc740 \ubaa8\ub450 \uc9c4\ub3d9\ud55c\ub2e4.<\/li>\n<li>\\(\\chi_\\mathbb{Q} : \\mathbb{R} \\rightarrow \\mathbb{R}\\)\uac00<br \/>\n\\[\\chi_\\mathbb{Q} (x) = \\begin{cases}<br \/>\n1 \\quad &#038; \\text{if}\\,\\,x\\in\\mathbb{Q} , \\\\<br \/>\n0 \\quad &#038; \\text{if}\\,\\,x\\notin\\mathbb{Q}<br \/>\n\\end{cases}\\]<br \/>\n\ub85c \uc815\uc758\ub41c \ud2b9\uc131\ud568\uc218(characteristic function)\ub77c\uba74 \uc784\uc758\uc758 \uc810 \\(c\\)\uc5d0\uc11c \\(\\chi_\\mathbb{Q}\\)\uc758 \uc88c\uadf9\ud55c\uacfc \uc6b0\uadf9\ud55c\uc740 \ubaa8\ub450 \uc9c4\ub3d9\ud55c\ub2e4.<\/li>\n<\/ol>\n<\/div>\n<p>\ub2e4\uc74c \uc815\ub9ac\ub294 \ud55c \ubc29\ud5a5 \uadf9\ud55c\uc758 \uc815\uc758\uc5d0 \uc758\ud558\uc5ec \uc790\uba85\ud558\uac8c \uc131\ub9bd\ud55c\ub2e4. (\uc99d\uba85\uc740 \uc0c1\uc704 \uacfc\uc815\uc5d0\uc11c \ud558\uaca0\ub2e4.)<\/p>\n<div class=\"theorem margintop2\">\n<p><span class=\"theorem\">\uc815\ub9ac 3.3.1. (\uc591 \ubc29\ud5a5 \uadf9\ud55c\uacfc \ud55c \ubc29\ud5a5 \uadf9\ud55c\uc758 \uad00\uacc4)<\/span><\/p>\n<p>\ud568\uc218 \\(f:D\\rightarrow \\mathbb{R}\\)\uac00 \uc8fc\uc5b4\uc84c\ub2e4\uace0 \ud558\uc790. \uadf8\ub9ac\uace0 \\(c\\)\uc5d0\uc11c \\(f\\)\uc758 \uc88c\uadf9\ud55c\uacfc \uc6b0\uadf9\ud55c\uc774 \uc815\uc758\ub41c\ub2e4\uace0 \ud558\uc790. [\uc989 \\(c\\)\uac00 \\((-\\infty ,\\,c)\\cap D\\)\uc758 \uc9d1\uc801\uc810\uc774\uba70, \\((c,\\,\\infty)\\cap D\\)\uc758 \uc9d1\uc801\uc810\uc774\ub2e4.] \uc774\ub54c<br \/>\n\\[\\lim_{x\\rightarrow c} f(x) = L\\]<br \/>\n\uc774\uae30 \uc704\ud55c \ud544\uc694\ucda9\ubd84\uc870\uac74\uc740<br \/>\n\\[\\lim_{x\\rightarrow c^-} f(x) = L \\quad\\text{and}\\quad \\lim_{x\\rightarrow c^+} f(x)=L\\]<br \/>\n\uc778 \uac83\uc774\ub2e4. \uc774\uac83\uc740 \\(L\\)\uc774 \uc2e4\uc218\uc77c \ub54c \ubfd0\ub9cc \uc544\ub2c8\ub77c, \\(L = \\infty\\)\uc774\uac70\ub098 \\(L = -\\infty\\)\uc77c \ub54c\ub3c4 \uc131\ub9bd\ud55c\ub2e4.\n<\/p>\n<\/div>\n<p>\uc218\uc5f4\uc758 \uadf9\ud55c\uc758 \ub2e8\uc870\uc218\ub834 \uc815\ub9ac\ucc98\ub7fc \ud568\uc218\uc758 \uadf9\ud55c\ub3c4 \ub2e8\uc870\uc218\ub834\uc744 \uc0dd\uac01\ud560 \uc218 \uc788\ub2e4.<\/p>\n<p>\ud568\uc218 \\(f\\)\uac00 \uc5f4\ub9b0\uad6c\uac04 \\(I=(a,\\,b)\\)\uc5d0\uc11c \uc815\uc758\ub418\uc5c8\ub2e4\uace0 \ud558\uc790. [\ubb3c\ub860 \\(a < b\\)\ub77c\uace0 \uac00\uc815\ud55c\ub2e4.] \uadf8\ub9ac\uace0 \\(f\\)\uac00 \\(I\\)\uc5d0\uc11c \ub2e8\uc870\uc99d\uac00\ud55c\ub2e4\uace0 \ud558\uc790. \uc989 \uc784\uc758\uc758 \\(s,\\,t\\in I\\)\uc5d0 \ub300\ud558\uc5ec\n\\[s\\le t \\quad\\Rightarrow\\quad f(s) \\le f(t)\\]\n\uac00 \uc131\ub9bd\ud55c\ub2e4\uace0 \ud558\uc790.<\/p>\n<p>\uc774\uc81c \\(c\\in I\\)\uac00 \uc784\uc758\ub85c \uc8fc\uc5b4\uc84c\ub2e4\uace0 \ud558\uc790.<\/p>\n<p class=\"aligncenter\">\u201c\ubaa8\ub4e0 \\(x\\in (a,\\,c)\\)\uc5d0 \ub300\ud558\uc5ec \\(f(x)\\le L\\)\u201d<\/p>\n<p>\uc744 \ub9cc\uc871\uc2dc\ud0a4\ub294 \\(L\\) \uc911\uc5d0\uc11c \uac00\uc7a5 \uc791\uc740 \uac83\uc744 \ud0dd\ud558\uc790. \uadf8\ub7ec\uba74 \\(x\\rightarrow c^-\\)\uc77c \ub54c \\(f(x)\\)\ub294 \\(L\\)\uc5d0 \uc218\ub834\ud55c\ub2e4. \uc65c\ub0d0\ud558\uba74, \ub9cc\uc57d \\(f(x)\\)\uac00 \\(L\\)\uc5d0 \uc218\ub834\ud558\uc9c0 \uc54a\ub294\ub2e4\uba74, \u201c\ubaa8\ub4e0 \\(x\\in (a,\\,c)\\)\uc5d0 \ub300\ud558\uc5ec \\(f(x)\\le L\\)\u201d\uc744 \ub9cc\uc871\uc2dc\ud0a4\ub294 \ub354 \uc791\uc740 \\(L\\)\uc744 \ud0dd\ud560 \uc218 \uc788\uae30 \ub54c\ubb38\uc774\ub2e4.<\/p>\n<p>\ub9c8\ucc2c\uac00\uc9c0\ub85c \u201c\ubaa8\ub4e0 \\(x\\in (c,\\,b)\\)\uc5d0 \ub300\ud558\uc5ec \\(f(x)\\ge M\\)\u201d\uc744 \ub9cc\uc871\uc2dc\ud0a4\ub294 \uac00\uc7a5 \ud070 \\(M\\)\uc744 \ud0dd\ud558\uba74 \\(x\\rightarrow c^+\\)\uc77c \ub54c \\(f(x)\\)\uac00 \\(M\\)\uc5d0 \uc218\ub834\ud55c\ub2e4.<\/p>\n<p>\\(f\\)\uac00 \\(I\\)\uc5d0\uc11c \ub2e8\uc870\uac10\uc18c\ud55c\ub2e4\uace0 \ud558\uc5ec\ub3c4 \uac19\uc740 \ub17c\ubc95\uc73c\ub85c \\(c\\)\uc5d0\uc11c \\(f\\)\uc758 \uc88c\uadf9\ud55c\uacfc \uc6b0\uadf9\ud55c\uc774 \ubaa8\ub450 \uc218\ub834\ud55c\ub2e4\ub294 \uacb0\ub860\uc744 \ub04c\uc5b4\ub0bc \uc218 \uc788\ub2e4.<\/p>\n<p>\uc774\ub85c\uc368 \ub2e4\uc74c \uc815\ub9ac\ub97c \uc99d\uba85\ud558\uc600\ub2e4.<\/p>\n<div class=\"theorem margintop2\">\n<p><span class=\"theorem\">\uc815\ub9ac 3.3.2. (\ub2e8\uc870\uc218\ub834 \uc815\ub9ac)<\/span><\/p>\n<p>\\(I\\)\uac00 \uae38\uc774\uac00 \uc591\uc218\uc778 \uc5f4\ub9b0\uad6c\uac04\uc774\ub77c\uace0 \ud558\uc790. \ud568\uc218 \\(f\\)\uac00 \\(I\\)\uc5d0\uc11c \ub2e8\uc870\uc774\uba74 \\(I\\)\uc758 \uc784\uc758\uc758 \uc810\uc5d0\uc11c \\(f\\)\uc758 \uc88c\uadf9\ud55c\uacfc \uc6b0\uadf9\ud55c\uc774 \ubaa8\ub450 \uc218\ub834\ud55c\ub2e4.<\/p>\n<\/div>\n<p><!-- ##################################################################### --><br \/>\n<!--\n\n\n<h2 class=\"itc_h2\">\uc81c\ubaa9<\/h2>\n\n\n\n\n\n<p>.<\/p>\n\n\n\n\n\n<p>.<\/p>\n\n\n--><\/p>\n<p><!--\n\n\n\n<div class=\"theorem margintop2\">\n\n\n<p><span class=\"theorem\">\uc815\ub9ac 1.<\/span>\n\n\n<\/p>\n\n<\/div>\n\n\n\n\n\n<div class=\"proof\">\n\n\n<p class=\"proofname\">\uc99d\uba85.<\/p>\n\n\n\n\n<p>\n\n<span class=\"qed\"><\/span><\/p>\n\n<\/div>\n\n\n\n\n########\n\n\u201c\u201d\n\u2018\u2019\n\n\n\n<div class=\"example\">\n\n\n<p><span class=\"example\">\ubcf4\uae30 1.<\/span>\n\n<\/p>\n\n<\/div>\n\n\n\n\n\n<h2 class=\"itc_h2\"><\/h2>\n\n\n\n--><\/p>\n<p><!--\n\n\n<div style=\"display: none; visibility: hidden;\">\n\\[\n\\newcommand{\\Hom}{{\\operatorname{Hom}}}\n\\newcommand{\\Mat}{{\\operatorname{Mat}}}\n\\newcommand{\\proj}{{\\operatorname{proj}}}\n\\newcommand{\\adj}{{\\operatorname{adj}}}\n\\]\n<\/div>\n\n\n--><\/p>\n<div class=\"box itc_prev_next_box\">\n<ul class=\"itc_ul\">\n<li class=\"itc_li_prev\">\uc55e\uc758 \uae00 : <a href=\"..\/properties-of-limit-of-a-function\">\ud568\uc218\uc758 \uadf9\ud55c\uc758 \uc131\uc9c8<\/a><\/li>\n<li class=\"itc_li_next\">\ub2e4\uc74c \uae00 : <a href=\"..\/limits-involving-infinity\">\ubb34\ud55c\ub300\ub97c \ud3ec\ud568\ud55c \uadf9\ud55c<\/a><\/li>\n<\/ul>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\uc774 \uae00\uc740 \u300e\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c\u300f 3\uc7a5 3\uc808\uc758 \ub0b4\uc6a9\uc785\ub2c8\ub2e4.&nbsp; (\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c \ucc28\ub840 \ubcf4\uae30) \uc810 \\(c\\)\uc5d0\uc11c \ud568\uc218 \\(f\\)\uc758 \uadf9\ud55c\uc744 \uc0dd\uac01\ud560 \ub54c, \\(x\\)\uac00 \\(c\\)\uc758 \uc67c\ucabd\uc73c\ub85c\ubd80\ud130 \\(c\\)\uc5d0 \ub2e4\uac00\uac00\ub294 \uacbd\uc6b0\uc640 \\(x\\)\uac00 \\(c\\)\uc758 \uc624\ub978\ucabd\uc73c\ub85c\ubd80\ud130 \\(c\\)\uc5d0 \ub2e4\uac00\uac00\ub294 \uacbd\uc6b0\ub97c \uc0dd\uac01\ud560 \uc218 \uc788\ub2e4. \\(f:D \\rightarrow \\mathbb{R}\\)\uac00 \ud568\uc218\uc774\uace0 \\(c\\)\uac00 \\(D\\)\uc758 \uc810\uc774\ub77c\uace0 \ud558\uc790. \ub9cc\uc57d \\(x\\)\uac00 \\(x < c\\)\ub97c \uc720\uc9c0\ud55c \ucc44\ub85c \\(c\\)\uc5d0 \ub2e4\uac00\uac08 \ub54c \\(f(x)\\)\uac00 \ud558\ub098\uc758 \uac12 \\(L\\)\uc5d0 \ub2e4\uac00\uac00\uba74, \\(L\\)\uc744 \\(c\\)\uc5d0\uc11c \\(f(x)\\)\uc758 \uc88c\uadf9\ud55c(left-sided limit)\uc774\ub77c\uace0 \ubd80\ub974\uace0, \uc774 \uc0c1\ud669\uc744&hellip;\n<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":6620,"menu_order":303,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_lmt_disableupdate":"","_lmt_disable":"","footnotes":""},"class_list":["post-6695","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6695","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/comments?post=6695"}],"version-history":[{"count":18,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6695\/revisions"}],"predecessor-version":[{"id":8386,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6695\/revisions\/8386"}],"up":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6620"}],"wp:attachment":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/media?parent=6695"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}