{"id":27904,"date":"2024-08-15T19:51:15","date_gmt":"2024-08-15T19:51:15","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=27904"},"modified":"2024-08-15T19:51:15","modified_gmt":"2024-08-15T19:51:15","slug":"%e0%a4%b9%e0%a4%b2-%e0%a4%95%e0%a5%80-%e0%a4%97%e0%a4%88-%e0%a4%b8%e0%a4%ae%e0%a4%b8%e0%a5%8d%e0%a4%af%e0%a4%be%e0%a4%8f%e0%a4%82-%e0%a4%b8%e0%a5%80%e0%a4%ae%e0%a4%bf%e0%a4%a4-%e0%a4%b8%e0%a5%80","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/hi\/%e0%a4%b9%e0%a4%b2-%e0%a4%95%e0%a5%80-%e0%a4%97%e0%a4%88-%e0%a4%b8%e0%a4%ae%e0%a4%b8%e0%a5%8d%e0%a4%af%e0%a4%be%e0%a4%8f%e0%a4%82-%e0%a4%b8%e0%a5%80%e0%a4%ae%e0%a4%bf%e0%a4%a4-%e0%a4%b8%e0%a5%80\/","title":{"rendered":"\u0939\u0932 \u0915\u0940 \u0917\u0908 \u0938\u092e\u0938\u094d\u092f\u093e\u090f\u0902: \u0938\u0940\u092e\u093f\u0924 \u0938\u0940\u092e\u093e\u090f\u0901"},"content":{"rendered":"<p><center><\/p>\n<h1>\u0939\u0932 \u0915\u0940 \u0917\u0908 \u0938\u092e\u0938\u094d\u092f\u093e\u090f\u0902: \u0938\u0940\u092e\u093f\u0924 \u0938\u0940\u092e\u093e\u090f\u0901<\/h1>\n<p><em><strong>\u0938\u093e\u0930\u093e\u0902\u0936:<\/strong><br \/>\n\u092f\u0939 \u0915\u0915\u094d\u0937\u093e \u0938\u0940\u092e\u093f\u0924 \u0938\u0940\u092e\u093e\u0913\u0902 \u0915\u0940 \u0917\u0923\u0928\u093e \u092a\u0930 \u0939\u0932 \u0915\u0940 \u0917\u0908 \u0938\u092e\u0938\u094d\u092f\u093e\u090f\u0902 \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u0930\u0924\u0940 \u0939\u0948, \u0938\u093e\u0925 \u0939\u0940 \u090f\u0915 \u0935\u0940\u0921\u093f\u092f\u094b \u091f\u094d\u092f\u0942\u091f\u094b\u0930\u093f\u092f\u0932 \u092d\u0940 \u0936\u093e\u092e\u093f\u0932 \u0939\u0948\u0964 \u091b\u093e\u0924\u094d\u0930\u094b\u0902 \u0915\u094b \u0938\u092e\u0938\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u0939\u0932 \u0915\u0930\u0928\u0947 \u0914\u0930 \u0909\u0928\u0915\u0947 \u092a\u0930\u093f\u0923\u093e\u092e\u094b\u0902 \u0915\u0940 \u0924\u0941\u0932\u0928\u093e \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u093f\u090f \u0917\u090f \u0938\u092e\u093e\u0927\u093e\u0928\u094b\u0902 \u0938\u0947 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092e\u093e\u0930\u094d\u0917\u0926\u0930\u094d\u0936\u0928 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0924\u0930\u094d\u0915\u0938\u0902\u0917\u0924\u0924\u093e \u0914\u0930 \u0917\u094d\u0930\u093e\u092b\u093c \u0915\u0947 \u0909\u092a\u092f\u094b\u0917 \u091c\u0948\u0938\u0940 \u092a\u094d\u0930\u092e\u0941\u0916 \u0924\u0915\u0928\u0940\u0915\u094b\u0902 \u092a\u0930 \u091c\u094b\u0930 \u0926\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u091c\u093f\u0938\u0938\u0947 \u0938\u0939\u0940 \u0909\u0924\u094d\u0924\u0930 \u0924\u0915 \u092a\u0939\u0941\u0901\u091a\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0926\u0943\u0937\u094d\u091f\u093f\u0915\u094b\u0923\u094b\u0902 \u0915\u094b \u092a\u094d\u0930\u094b\u0924\u094d\u0938\u093e\u0939\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/em><\/p>\n<p><strong>\u0938\u0940\u0916\u0928\u0947 \u0915\u0947 \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f<\/strong><br \/>\n\u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u0915\u0947 \u0905\u0902\u0924 \u0924\u0915, \u091b\u093e\u0924\u094d\u0930 \u0938\u0915\u094d\u0937\u092e \u0939\u094b\u0902\u0917\u0947:<\/p>\n<ul style=\"text-align:left;\">\n<li><strong>\u092c\u0939\u0941\u092a\u0926 \u0914\u0930 \u092f\u0941\u0915\u094d\u0924\u093f\u0915\u093e\u0930\u0940 \u0915\u093e\u0930\u094d\u092f\u094b\u0902<\/strong> \u0915\u0940 \u0938\u0940\u092e\u093f\u0924 \u0938\u0940\u092e\u093e\u0913\u0902 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0947\u0902\u0964<\/li>\n<li><strong>\u0938\u0940\u092e\u093e \u0917\u0923\u0928\u093e<\/strong> \u0915\u094b \u0938\u0930\u0932 \u092c\u0928\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0924\u0930\u094d\u0915\u0938\u0902\u0917\u0924 \u0924\u0915\u0928\u0940\u0915\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902\u0964<\/li>\n<li><strong>\u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0938\u092e\u093e\u0927\u093e\u0928 \u0935\u093f\u0927\u093f\u092f\u094b\u0902<\/strong> \u0915\u0940 \u0924\u0941\u0932\u0928\u093e \u0915\u0930\u0947\u0902 \u0914\u0930 \u0938\u0939\u0940 \u0938\u092e\u093e\u0927\u093e\u0928 \u0924\u0915 \u092a\u0939\u0941\u0901\u091a\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u0908 \u092e\u093e\u0930\u094d\u0917\u094b\u0902 \u0915\u0940 \u092a\u0939\u091a\u093e\u0928 \u0915\u0930\u0947\u0902\u0964<\/li>\n<\/ul>\n<p><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/VY1gr1EUq3o\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\n<\/center><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u092f\u0947 \u0939\u0932 \u0915\u093f\u090f \u0917\u090f \u0905\u092d\u094d\u092f\u093e\u0938 \u0906\u092a\u0915\u094b \u0938\u0940\u092e\u093f\u0924 \u0938\u0940\u092e\u093e\u0913\u0902 \u0915\u0940 \u0917\u0923\u0928\u093e \u092e\u0947\u0902 \u092e\u0939\u093e\u0930\u0924 \u0939\u093e\u0938\u093f\u0932 \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u092e\u0926\u0926 \u0915\u0930\u0947\u0902\u0917\u0947\u0964 \u0938\u092e\u093e\u0927\u093e\u0928 \u0935\u0940\u0921\u093f\u092f\u094b \u092e\u0947\u0902 \u0939\u0948\u0902\u0964<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0936\u093f\u0915\u094d\u0937\u0923 \u0905\u0928\u0941\u092d\u0935 \u0915\u094b \u092c\u0947\u0939\u0924\u0930 \u092c\u0928\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u092e\u0948\u0902\u0928\u0947 \u0938\u0940\u092e\u093e\u0913\u0902 \u0915\u0940 \u0917\u0923\u0928\u093e \u092a\u0930 \u0939\u0932 \u0915\u093f\u090f \u0917\u090f \u0905\u092d\u094d\u092f\u093e\u0938\u094b\u0902 \u0935\u093e\u0932\u093e \u092f\u0939 \u0935\u0940\u0921\u093f\u092f\u094b \u092c\u0928\u093e\u092f\u093e \u0939\u0948, \u091c\u093f\u0938\u092e\u0947\u0902 \u0909\u0928 \u0938\u092d\u0940 \u0935\u093f\u0936\u0947\u0937\u0924\u093e\u0913\u0902 \u0915\u094b \u0926\u093f\u0916\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948 \u091c\u093f\u0928\u094d\u0939\u0947\u0902 \u0909\u0928\u0938\u0947 \u0928\u093f\u0915\u093e\u0932\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0907\u0928 \u0905\u092d\u094d\u092f\u093e\u0938\u094b\u0902 \u0915\u094b \u0938\u094d\u0935\u092f\u0902 \u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u093e \u092a\u094d\u0930\u092f\u093e\u0938 \u0915\u0930\u0947\u0902 \u0914\u0930 \u092b\u093f\u0930 \u0905\u092a\u0928\u0947 \u092a\u0930\u093f\u0923\u093e\u092e\u094b\u0902 \u0915\u0940 \u0924\u0941\u0932\u0928\u093e \u0915\u0930\u0947\u0902\u0964<br \/>\n\u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0905\u092d\u094d\u092f\u093e\u0938 \u0915\u0947 \u092c\u0917\u0932 \u092e\u0947\u0902, \u0906\u092a\u0915\u094b \u090f\u0915 \u0932\u093f\u0902\u0915 \u092e\u093f\u0932\u0947\u0917\u093e \u091c\u094b YouTube \u0935\u0940\u0921\u093f\u092f\u094b \u0915\u0947 \u0909\u0938 \u0939\u093f\u0938\u094d\u0938\u0947 \u0915\u0940 \u0913\u0930 \u0932\u0947 \u091c\u093e\u0924\u093e \u0939\u0948 \u091c\u0939\u093e\u0901 \u0938\u092d\u0940 \u0917\u0923\u0928\u093e\u090f\u0901 \u0938\u092e\u093e\u0927\u093e\u0928 \u0924\u0915 \u0915\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948\u0902\u0964<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0915\u092d\u0940-\u0915\u092d\u0940 \u0906\u092a\u0915\u094b \u0924\u0930\u094d\u0915\u0938\u0902\u0917\u0924 \u092c\u0928\u093e\u0928\u093e \u0939\u094b\u0917\u093e, \u0914\u0930 \u0905\u0928\u094d\u092f \u0938\u092e\u092f \u092e\u0947\u0902 \u0906\u092a\u0915\u094b \u0909\u0924\u094d\u0924\u0930 \u0915\u094b \u0938\u0939\u0940 \u0920\u0939\u0930\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0938\u0940\u092e\u093e \u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u092a\u0930 \u092d\u0930\u094b\u0938\u093e \u0915\u0930\u0928\u093e \u0939\u094b\u0917\u093e\u0964 \u0915\u092d\u0940-\u0915\u092d\u0940, \u090f\u0915 \u0917\u094d\u0930\u093e\u092b \u092d\u0940 \u0906\u092a\u0915\u094b \u092f\u0939 \u0924\u092f \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u092c\u0939\u0941\u0924 \u0938\u093e\u0930\u093e \u0915\u093e\u092e \u092c\u091a\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u0915\u093f \u0915\u093f\u0938 \u0924\u0930\u094d\u0915 \u092a\u0925 \u0915\u093e \u092a\u093e\u0932\u0928 \u0915\u0930\u0928\u093e \u0939\u0948\u0964<\/p>\n<h3>\u092a\u0939\u0932\u093e: \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u0940\u092e\u093f\u0924 \u0938\u0940\u092e\u093e\u0913\u0902 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0947\u0902:<\/h3>\n<ol style=\"text-align: justify; color: #000000;\">\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to -1} (x^3+2x^2 - 3x - 4) <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=VY1gr1EUq3o&amp;t=35s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">[\u0938\u092e\u093e\u0927\u093e\u0928]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to 0} \\dfrac{3^x - 3^{-x}}{3^x + 3^{-x}} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=VY1gr1EUq3o&amp;t=64s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">[\u0938\u092e\u093e\u0927\u093e\u0928]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to 2} \\dfrac{x-1}{x^2-1} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=VY1gr1EUq3o&amp;t=91s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">[\u0938\u092e\u093e\u0927\u093e\u0928]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to 2} \\dfrac{x^2-4}{x^2-5x+6} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=VY1gr1EUq3o&amp;t=161s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">[\u0938\u092e\u093e\u0927\u093e\u0928]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to -1} \\dfrac{x^2+3x+2}{x^2+4x+3} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=VY1gr1EUq3o&amp;t=351s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">[\u0938\u092e\u093e\u0927\u093e\u0928]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to 2} \\dfrac{x-2}{\\sqrt{x^2-4}} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=VY1gr1EUq3o&amp;t=594s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">[\u0938\u092e\u093e\u0927\u093e\u0928]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to 2} \\dfrac{\\sqrt{x-2}}{x^2-4} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=VY1gr1EUq3o&amp;t=887s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">[\u0938\u092e\u093e\u0927\u093e\u0928]<\/span><\/strong><\/a><\/li>\n<\/ol>\n<h3>\u0926\u0942\u0938\u0930\u093e: \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0915\u093e\u0930\u094d\u092f\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{h\\to 0} \\frac{f(x+h)-f(x)}{h}<\/span><\/span> \u0922\u0942\u0902\u0922\u0947\u0902:<\/h3>\n<ol style=\"text-align: justify; color: #000000;\">\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle f(x) = \\dfrac{1}{x-2} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=VY1gr1EUq3o&amp;t=1088s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">[\u0938\u092e\u093e\u0927\u093e\u0928]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle f(x) = \\sqrt{x-4} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=VY1gr1EUq3o&amp;t=1263s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">[\u0938\u092e\u093e\u0927\u093e\u0928]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle f(x) = \\dfrac{x}{x+1} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=VY1gr1EUq3o&amp;t=1366s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">[\u0938\u092e\u093e\u0927\u093e\u0928]<\/span><\/strong><\/a><\/li>\n<\/ol>\n<p style=\"text-align: justify; color: #000000;\">\u0915\u094d\u092f\u093e \u0906\u092a \u0909\u0928\u094d\u0939\u0947\u0902 \u0938\u092d\u0940 \u0915\u094b \u0938\u094d\u0935\u092f\u0902 \u0939\u0932 \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u0938\u092b\u0932 \u0930\u0939\u0947?<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0906\u092a\u0915\u0947 \u0938\u092e\u093e\u0927\u093e\u0928 \u092e\u0947\u0930\u0947 \u0938\u0947 \u0915\u093f\u0924\u0928\u0947 \u0905\u0932\u0917 \u0939\u0948\u0902?<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u092f\u093e\u0926 \u0930\u0916\u0947\u0902 \u0915\u093f \u0938\u092e\u0938\u094d\u092f\u093e \u0915\u094b \u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u093e \u0930\u093e\u0938\u094d\u0924\u093e \u091c\u0930\u0942\u0930\u0940 \u0928\u0939\u0940\u0902 \u0915\u093f \u090f\u0915 \u0939\u0940 \u0939\u094b\u0964<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0939\u0932 \u0915\u0940 \u0917\u0908 \u0938\u092e\u0938\u094d\u092f\u093e\u090f\u0902: \u0938\u0940\u092e\u093f\u0924 \u0938\u0940\u092e\u093e\u090f\u0901 \u0938\u093e\u0930\u093e\u0902\u0936: \u092f\u0939 \u0915\u0915\u094d\u0937\u093e \u0938\u0940\u092e\u093f\u0924 \u0938\u0940\u092e\u093e\u0913\u0902 \u0915\u0940 \u0917\u0923\u0928\u093e \u092a\u0930 \u0939\u0932 \u0915\u0940 \u0917\u0908 \u0938\u092e\u0938\u094d\u092f\u093e\u090f\u0902 \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u0930\u0924\u0940 \u0939\u0948, \u0938\u093e\u0925 \u0939\u0940 \u090f\u0915 \u0935\u0940\u0921\u093f\u092f\u094b \u091f\u094d\u092f\u0942\u091f\u094b\u0930\u093f\u092f\u0932 \u092d\u0940 \u0936\u093e\u092e\u093f\u0932 \u0939\u0948\u0964 \u091b\u093e\u0924\u094d\u0930\u094b\u0902 \u0915\u094b \u0938\u092e\u0938\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u0939\u0932 \u0915\u0930\u0928\u0947 \u0914\u0930 \u0909\u0928\u0915\u0947 \u092a\u0930\u093f\u0923\u093e\u092e\u094b\u0902 \u0915\u0940 \u0924\u0941\u0932\u0928\u093e \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u093f\u090f \u0917\u090f \u0938\u092e\u093e\u0927\u093e\u0928\u094b\u0902 \u0938\u0947 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092e\u093e\u0930\u094d\u0917\u0926\u0930\u094d\u0936\u0928 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0924\u0930\u094d\u0915\u0938\u0902\u0917\u0924\u0924\u093e \u0914\u0930 \u0917\u094d\u0930\u093e\u092b\u093c [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":27893,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":0,"footnotes":""},"categories":[862,577],"tags":[],"class_list":["post-27904","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-862","category-577"],"yoast_head":"<!-- This site is optimized with the Yoast SEO 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