{"id":50492,"date":"2021-05-26T12:47:29","date_gmt":"2021-05-26T07:17:29","guid":{"rendered":"https:\/\/samacheerguru.com\/?p=50492"},"modified":"2021-05-26T12:49:40","modified_gmt":"2021-05-26T07:19:40","slug":"samacheer-kalvi-11th-maths-guide-chapter-9-ex-9-3-in-tamil","status":"publish","type":"post","link":"https:\/\/samacheerguru.com\/samacheer-kalvi-11th-maths-guide-chapter-9-ex-9-3-in-tamil\/","title":{"rendered":"Samacheer Kalvi 11th Maths Guide Chapter 9 \u0b95\u0ba3\u0b99\u0bcd\u0b95\u0bb3\u0bcd, \u0ba4\u0bca\u0b9f\u0bb0\u0bcd\u0baa\u0bc1\u0b95\u0bb3\u0bcd \u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd \u0b9a\u0bbe\u0bb0\u0bcd\u0baa\u0bc1\u0b95\u0bb3\u0bcd Ex 9.3"},"content":{"rendered":"

Tamilnadu State Board New Syllabus Samacheer Kalvi 11th Maths Guide<\/a> Pdf Chapter 9 \u0b95\u0ba3\u0b99\u0bcd\u0b95\u0bb3\u0bcd, \u0ba4\u0bca\u0b9f\u0bb0\u0bcd\u0baa\u0bc1\u0b95\u0bb3\u0bcd \u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd na\u0b9a\u0bbe\u0bb0\u0bcd\u0baa\u0bc1\u0b95\u0bb3\u0bcd Ex 9.3 Textbook Questions and Answers, Notes.<\/p>\n

TN Board 11th Maths Solutions Chapter 9 \u0b95\u0ba3\u0b99\u0bcd\u0b95\u0bb3\u0bcd, \u0ba4\u0bca\u0b9f\u0bb0\u0bcd\u0baa\u0bc1\u0b95\u0bb3\u0bcd \u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd \u0b9a\u0bbe\u0bb0\u0bcd\u0baa\u0bc1\u0b95\u0bb3\u0bcd Ex 9.3<\/h2>\n

Question 1.
\n\u0baa\u0bbf\u0ba9\u0bcd\u0bb5\u0bb0\u0bc1\u0bae\u0bcd \u0b9a\u0bbe\u0bb0\u0bcd\u0baa\u0bc1\u0b95\u0bb3\u0bc1\u0b95\u0bcd\u0b95\u0bc1 \u0b87\u0b9f\u0baa\u0bcd\u0baa\u0bc1\u0bb1, \u0bb5\u0bb2\u0baa\u0bcd\u0baa\u0bc1\u0bb1 \u0b8e\u0bb2\u0bcd\u0bb2\u0bc8\u0b95\u0bb3\u0bbf\u0bb2\u0bcd \u0bae\u0ba4\u0bbf\u0baa\u0bcd\u0baa\u0bc8\u0b95\u0bcd \u0b95\u0bbe\u0ba3\u0bcd\u0b95
\n(a) x = -2-\u0bb2\u0bcd f(x) = \\(\\frac{x^{2}-4}{\\left(x^{2}+4 x+4\\right)(x+3)}\\)
\n(b) x = \\(\\frac{\\pi}{2}\\)-\u0bb2\u0bcd f(x) = tan x<\/p>\n

(a) x = -2-\u0bb2\u0bcd f(x) = \\(\\frac{x^{2}-4}{\\left(x^{2}+4 x+4\\right)(x+3)}\\)
\n\u0ba4\u0bc0\u0bb0\u0bcd\u0bb5\u0bc1 :
\nf(x) = \\(\\frac{x^{2}-4}{\\left(x^{2}+4 x+4\\right)(x+3)}\\)
\nf(-2–<\/sup>) = \"Samacheer
\n= \\(\\lim _{x \\rightarrow-2^{-}} \\frac{x-2}{(x+2)(x+3)}\\)
\n= \\(\\frac{-V e}{0(-V e)}\\) = \u221e
\n\u2234 f(-2–<\/sup>) \u2192 \u221e (x \u2192 -2–<\/sup> \u0b8e\u0ba9\u0bc1\u0bae\u0bcd \u0baa\u0bca\u0bb4\u0bc1\u0ba4\u0bc1 )
\nf(-2+<\/sup>) = \"Samacheer
\nf(-2+<\/sup>) = \\(\\lim _{x \\rightarrow-2^{+}} \\frac{x-2}{(x+2)(x+3)}\\)
\n= \"Samacheer = – \u221e
\n\u2234 f(-2+<\/sup>) \u2192 \u221e (x \u2192 -2+<\/sup> \u0b8e\u0ba9\u0bc1\u0bae\u0bcd \u0baa\u0bca\u0bb4\u0bc1\u0ba4\u0bc1 )<\/p>\n

(b) f(x) = tan x at x = \\(\\frac{\\pi}{2}\\)
\nf(x) = tan x
\nx = \\(\\frac{\\pi}{2}\\)-\u0bb2\u0bcd f(x) = tan x \u0b90\u0b95\u0bcd \u0b95\u0bbe\u0bb3\u0bc8
\n\\(\\lim _{x \\rightarrow \\frac{\\pi}{2}^{-}}\\) f(x) = \\(\\lim _{x \\rightarrow \\frac{\\pi}{2}^{-}}\\) tan x = \u221e
\n\u2234 \\(\\lim _{x \\rightarrow \\frac{\\pi}{2}^{-}}\\) f(x) \u2192 \u221e<\/p>\n

\\(\\lim _{x \\rightarrow \\frac{\\pi}{2}^{+}}\\) f(x) = \\(\\lim _{x \\rightarrow \\frac{\\pi}{2}^{+}}\\) tan x = – \u221e
\n\u2234 \\(\\lim _{x \\rightarrow \\frac{\\pi}{2}^{+}}\\) f(x) \u2192 – \u221e
\n\u0baa\u0bbf\u0ba9\u0bcd\u0bb5\u0bb0\u0bc1\u0bae\u0bcd \u0b8e\u0bb2\u0bcd\u0bb2\u0bc8\u0b95\u0bb3\u0bbf\u0ba9\u0bcd \u0bae\u0ba4\u0bbf\u0baa\u0bcd\u0baa\u0bc8\u0b95\u0bcd \u0b95\u0bbe\u0ba3\u0bcd\u0b95<\/p>\n

\"Samacheer<\/p>\n

Question 2.
\n\\(\\lim _{x \\rightarrow 3} \\frac{x^{2}-9}{x^{2}\\left(x^{2}-6 x+9\\right)}\\)
\n\u0ba4\u0bc0\u0bb0\u0bcd\u0bb5\u0bc1 :
\n\\(\\lim _{x \\rightarrow 3^{-}} f(x)=\\lim _{x \\rightarrow 3^{-}} \\frac{x^{2}-9}{x^{2}\\left(x^{2}-6 x+9\\right)}\\)
\n= \"Samacheer
\n= \\(\\lim _{x \\rightarrow 3^{-}} \\frac{x+3}{x^{2}(x-3)}\\)
\n= \\(\\frac{6}{\\not 6^{\\prime}(3-3)}=-\\frac{2}{0}\\) = – \u221e
\nx \u2192 3–<\/sup> \u0b8e\u0ba9\u0bbf\u0bb2\u0bcd f (3) \u2192 – \u221e
\n\\(\\lim _{x \\rightarrow 3^{+}}\\) f(x) = \\(\\lim _{x \\rightarrow 3^{+}} \\frac{x+3}{x^{2}(x-3)}\\) = \u221e<\/p>\n

Question 3.
\n\\(\\lim _{x \\rightarrow \\infty} \\frac{3}{x-2}-\\frac{2 x+11}{x^{2}+x-6}\\)
\n\u0ba4\u0bc0\u0bb0\u0bcd\u0bb5\u0bc1 :<\/p>\n

\"Samacheer<\/p>\n

Question 4.
\n\\(\\lim _{x \\rightarrow \\infty} \\frac{x^{3}+x}{x^{4}-3 x^{2}+1}\\)
\n\u0ba4\u0bc0\u0bb0\u0bcd\u0bb5\u0bc1 :
\n\\(\\lim _{x \\rightarrow \\infty} \\frac{x^{3}+x}{x^{4}-3 x^{2}+1}\\)
\n\u0ba4\u0bca\u0b95\u0bc1\u0ba4\u0bbf\u0baf\u0bbf\u0bb2\u0bbf\u0bb0\u0bc1\u0ba8\u0bcd\u0ba4\u0bc1 x3<\/sup>, \u0baa\u0b95\u0bc1\u0ba4\u0bbf\u0baf\u0bbf\u0bb2\u0bbf\u0bb0\u0bc1\u0ba8\u0bcd\u0ba4\u0bc1 x4<\/sup> \u0b90 \u0bb5\u0bc6\u0bb3\u0bbf\u0baf\u0bbf\u0bb2\u0bcd \u0b8e\u0b9f\u0bc1\u0b95\u0bcd\u0b95<\/p>\n

= \\(\\lim _{x \\rightarrow \\infty} \\frac{x^{3}\\left(1+\\frac{1}{x^{2}}\\right)}{x^{4}\\left(1-\\frac{3}{x^{2}}+\\frac{1}{x^{4}}\\right)}\\)<\/p>\n

= \\(\\lim _{x \\rightarrow \\infty} \\frac{\\left(1+\\frac{1}{x^{2}}\\right)}{x\\left(1-\\frac{3}{x^{2}}+\\frac{1}{x^{4}}\\right)}=\\frac{1}{\\infty}\\) = 0
\n[\u2235 \\(\\frac{1}{x}\\) \u2192 0; x \u2192 \u221e]<\/p>\n

\u2234 \\(\\lim _{x \\rightarrow \\infty} \\frac{x^{3}+x}{x^{4}-3 x^{2}+1}\\) = 0<\/p>\n

\"Samacheer<\/p>\n

Question 5.
\n\\(\\lim _{x \\rightarrow \\infty} \\frac{x^{4}-5 x}{x^{2}-3 x+1}\\)
\n\u0ba4\u0bc0\u0bb0\u0bcd\u0bb5\u0bc1 :
\n\\(\\lim _{x \\rightarrow \\infty} \\frac{x^{4}-5 x}{x^{2}-3 x+1}\\) = \\(\\lim _{x \\rightarrow \\infty} \\frac{x^{4}\\left(1-\\frac{5}{x^{3}}\\right)}{x^{2}\\left(1-\\frac{3}{x}+\\frac{1}{x^{2}}\\right)}\\)<\/p>\n

= \\(\\lim _{x \\rightarrow \\infty} \\frac{x^{2}\\left(1-\\frac{5}{x^{3}}\\right)}{\\left(1-\\frac{3}{x}+\\frac{1}{x^{2}}\\right)}\\) = \u221e
\n[\u2235 \\(\\frac{1}{x}\\) \u2192 0; x \u2192 \u221e]<\/p>\n

\\(\\lim _{x \\rightarrow \\infty} \\frac{x^{4}-5 x}{x^{2}-3 x+1}\\) = \u221e<\/p>\n

Question 6.
\n\\(\\lim _{x \\rightarrow \\infty} \\frac{1+x-3 x^{3}}{1+x^{2}+3 x^{3}}\\)
\n\u0ba4\u0bc0\u0bb0\u0bcd\u0bb5\u0bc1 :<\/p>\n

\"Samacheer<\/p>\n

Question 7.
\n\\(\\lim _{x \\rightarrow \\infty}\\left(\\frac{x^{3}}{2 x^{2}-1}-\\frac{x^{2}}{2 x+1}\\right)\\)
\n\u0ba4\u0bc0\u0bb0\u0bcd\u0bb5\u0bc1 :<\/p>\n

\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 8.
\n\u0ba8\u0bbf\u0bb1\u0bc1\u0bb5\u0bc1\u0b95
\n(i) \\(\\lim _{n \\rightarrow \\infty} \\frac{1+2+3+\\ldots+n}{3 n^{2}+7 n+2}=\\frac{1}{6}\\)
\n(ii) \\(\\lim _{n \\rightarrow \\infty} \\frac{1^{2}+2^{2}+\\ldots+(3 n)^{2}}{(1+2+\\ldots+5 n)(2 n+3)}=\\frac{9}{25}\\)
\n(iii) \\(\\lim _{n \\rightarrow \\infty} \\frac{1}{1.2}+\\frac{1}{2.3}+\\frac{1}{3.4}+\\ldots+\\frac{1}{n(n+1)}=1\\)
\n\u0ba4\u0bc0\u0bb0\u0bcd\u0bb5\u0bc1 :
\n(i) \\(\\lim _{n \\rightarrow \\infty} \\frac{1+2+3+\\ldots+n}{3 n^{2}+7 n+2}=\\frac{1}{6}\\)
\n\\(\\lim _{n \\rightarrow \\infty} \\frac{1+2+3+\\ldots+n}{3 n^{2}+7 n+2}\\) = \\(\\lim _{n \\rightarrow \\infty} \\frac{\\frac{n(n+1)}{2}}{3 n^{2}+7 n+2}\\)
\n[\u2235 \u03a3n = \\(\\frac{n(n+1)}{2}\\)]
\n= \"Samacheer
\n= \\(\\frac{1}{2} \\lim _{n \\rightarrow \\infty} \\frac{\\left(1+\\frac{1}{n}\\right)}{\\left(3+\\frac{7}{n}+\\frac{2}{n^{2}}\\right)}\\)
\n= \\(\\frac{1}{2}\\) \u00d7 \\(\\frac{1}{3}\\) = \\(\\frac{1}{6}\\) = RHS
\n\u2234 \u0b8e\u0ba9\u0bb5\u0bc7 \u0ba8\u0bbf\u0bb0\u0bc1\u0baa\u0bbf\u0b95\u0bcd\u0b95\u0baa\u0bcd\u0baa\u0b9f\u0bcd\u0b9f\u0ba4\u0bc1.<\/p>\n

(ii) \\(\\lim _{n \\rightarrow \\infty} \\frac{1^{2}+2^{2}+\\ldots+(3 n)^{2}}{(1+2+\\ldots+5 n)(2 n+3)}=\\frac{9}{25}\\)
\n\"Samacheer<\/p>\n

(iii) \\(\\lim _{n \\rightarrow \\infty} \\frac{1}{1.2}+\\frac{1}{2.3}+\\frac{1}{3.4}+\\ldots+\\frac{1}{n(n+1)}=1\\)
\nLHS = \\(\\lim _{n \\rightarrow \\infty} \\frac{1}{1.2}+\\frac{1}{2.3}+\\frac{1}{3.4}+\\ldots+\\frac{1}{n(n+1)}\\)
\n= \\(\\lim _{n \\rightarrow \\infty} \\Sigma \\frac{1}{n(n+1)}=\\lim _{n \\rightarrow \\infty} \\frac{1}{n^{2}+n}\\)<\/p>\n

\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 9.
\n\u0bae\u0bc0\u0ba9\u0bcd \u0bb5\u0bb3 \u0b85\u0bb1\u0bbf\u0bb5\u0bbf\u0baf\u0bb2\u0bbf\u0ba9\u0bcd \u0bae\u0bc1\u0b95\u0bcd\u0b95\u0bbf\u0baf \u0baa\u0bbf\u0bb0\u0b9a\u0bcd\u0b9a\u0ba9\u0bc8 \u0ba8\u0bc0\u0bb0\u0bcb\u0b9f\u0bc8\u0b95\u0bb3\u0bbf\u0bb2\u0bcd \u0b89\u0bb3\u0bcd\u0bb3 \u0bae\u0bc1\u0b9f\u0bcd\u0b9f\u0bc8\u0baf\u0bbf\u0b9f\u0ba4\u0bcd \u0ba4\u0b95\u0bc1\u0ba4\u0bbf\u0baf\u0bbe\u0ba9 \u0bae\u0bc0\u0ba9\u0bcd\u0b95\u0bb3\u0bbf\u0ba9\u0bcd \u0b8e\u0ba3\u0bcd\u0ba3\u0bbf\u0b95\u0bcd\u0b95\u0bc8\u0baf\u0bc8\u0b95\u0bcd \u0b95\u0ba3\u0b95\u0bcd\u0b95\u0bbf\u0b9f\u0bcd\u0b9f\u0bc1 \u0b87\u0ba8\u0bcd\u0ba4\u0ba4\u0bcd \u0ba4\u0b95\u0bb5\u0bb2\u0bc8\u0baa\u0bcd \u0baa\u0baf\u0ba9\u0bcd\u0baa\u0b9f\u0bc1\u0ba4\u0bcd\u0ba4\u0bbf \u0b87\u0ba9\u0baa\u0bcd\u0baa\u0bc6\u0bb0\u0bc1\u0b95\u0bcd\u0b95\u0b95\u0bcd \u0b95\u0bbe\u0bb2\u0ba4\u0bcd\u0ba4\u0bbf\u0bb2\u0bcd \u0b86\u0bb1\u0bcd\u0bb1\u0bc1\u0b95\u0bcd\u0b95\u0bc1\u0bb3\u0bcd \u0ba8\u0bc1\u0bb4\u0bc8\u0baf\u0bc1\u0bae\u0bcd \u0bae\u0bc0\u0ba9\u0bcd \u0baa\u0bbf\u0b9f\u0bbf\u0baa\u0bcd\u0baa\u0bc1\u0b95\u0bcd\u0b95\u0bc1\u0ba4\u0bcd \u0ba4\u0b95\u0bc1\u0ba8\u0bcd\u0ba4 \u0bae\u0bc0\u0ba9\u0bcd\u0b95\u0bb3\u0bbf\u0ba9\u0bcd \u0b8e\u0ba3\u0bcd\u0ba3\u0bbf\u0b95\u0bcd\u0b95\u0bc8\u0baf\u0bc8\u0b95\u0bcd \u0b95\u0ba3\u0b95\u0bcd\u0b95\u0bbf\u0b9f\u0bc1\u0bb5\u0ba4\u0bbe\u0b95\u0bc1\u0bae\u0bcd.<\/p>\n

S \u0b8e\u0ba9\u0bcd\u0baa\u0ba4\u0bc1 \u0bae\u0bc1\u0b9f\u0bcd\u0b9f\u0bc8\u0baf\u0bbf\u0b9f\u0bc1\u0bae\u0bcd \u0ba8\u0bbf\u0bb2\u0bc8\u0baf\u0bbf\u0bb2\u0bcd \u0b89\u0bb3\u0bcd\u0bb3 \u0bae\u0bc0\u0ba9\u0bcd\u0b95\u0bb3\u0bbf\u0ba9\u0bcd \u0b8e\u0ba3\u0bcd\u0ba3\u0bbf\u0b95\u0bcd\u0b95\u0bc8 \u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd R \u0b8e\u0ba9\u0bcd\u0baa\u0ba4\u0bc1 \u0bae\u0bc0\u0ba9\u0bcd \u0baa\u0bbf\u0b9f\u0bbf\u0baa\u0bcd\u0baa\u0bc1\u0b95\u0bcd\u0b95\u0bc1 \u0ba4\u0b95\u0bc1\u0ba8\u0bcd\u0ba4 \u0bae\u0bc0\u0ba9\u0bcd\u0b95\u0bb3\u0bbf\u0ba9\u0bcd \u0b8e\u0ba3\u0bcd\u0ba3\u0bbf\u0b95\u0bcd\u0b95\u0bc8\u0baf\u0bbe\u0b95\u0bc1\u0bae\u0bcd. “\u0baa\u0bbf\u0bb5\u0bb0\u0bcd\u0b9f\u0bcd\u0b9f\u0ba9\u0bcd \u0bb9\u0bcb\u0bb2\u0bcd\u0b9f\u0bcd\u201d\u0ba9\u0bcd \u0b87\u0ba9\u0baa\u0bcd\u0baa\u0bc6\u0bb0\u0bc1\u0b95\u0bcd\u0b95\u0b9a\u0bcd \u0b9a\u0bbe\u0bb0\u0bcd\u0baa\u0bc1 R(S) = \\(\\frac{\\mathbf{S}}{(\\alpha \\mathbf{S}+\\beta)}\\) \u0baa\u0bbe \u0b87\u0b99\u0bcd\u0b95\u0bc1 \u03b1 \u03b2 \u0b8e\u0ba9\u0bcd\u0baa\u0ba9 \u0bae\u0bbf\u0b95\u0bc8 \u0bae\u0bbe\u0bb1\u0bbf\u0bb2\u0bbf\u0b95\u0bb3\u0bcd. \u0b87\u0ba8\u0bcd\u0ba4\u0b9a\u0bcd \u0b9a\u0bbe\u0bb0\u0bcd\u0baa\u0bc1 \u0b87\u0ba9\u0baa\u0bcd\u0baa\u0bc6\u0bb0\u0bc1\u0b95\u0bcd\u0b95 \u0ba8\u0bbf\u0bb2\u0bc8\u0baf\u0bbf\u0bb2\u0bcd \u0b87\u0bb0\u0bc1\u0b95\u0bcd\u0b95\u0bc1\u0bae\u0bcd \u0bae\u0bc0\u0ba9\u0bcd\u0b95\u0bb3\u0bbf\u0ba9\u0bcd \u0b8e\u0ba3\u0bcd\u0ba3\u0bbf\u0b95\u0bcd\u0b95\u0bc8 \u0ba4\u0bc7\u0bb5\u0bc8\u0baf\u0bbe\u0ba9 \u0b85\u0bb3\u0bb5\u0bc1 \u0b85\u0ba4\u0bbf\u0b95\u0bb0\u0bbf\u0b95\u0bcd\u0b95\u0bc1\u0bae\u0bcd \u0baa\u0bcb\u0ba4\u0bc1 \u0b85\u0bb1\u0bc1\u0bb5\u0b9f\u0bc8\u0b95\u0bcd\u0b95\u0bc1\u0ba4\u0bcd \u0ba4\u0b95\u0bc1\u0ba8\u0bcd\u0ba4 \u0bae\u0bc0\u0ba9\u0bcd\u0b95\u0bb3\u0bbf\u0ba9\u0bcd \u0b8e\u0ba3\u0bcd\u0ba3\u0bbf\u0b95\u0bcd\u0b95\u0bc8 \u0ba4\u0bcb\u0bb0\u0bbe\u0baf\u0bae\u0bbe\u0b95 \u0bae\u0bbe\u0bb1\u0bbf\u0bb2\u0bbf\u0baf\u0bbe\u0b95 \u0b85\u0bae\u0bc8\u0baf\u0bc1\u0bae\u0bcd \u0b8e\u0ba9 \u0ba8\u0bbf\u0bb1\u0bc1\u0bb5\u0bc1\u0b95.
\n\u0ba4\u0bc0\u0bb0\u0bcd\u0bb5\u0bc1 :
\nR(S) = \\(\\frac{\\mathbf{S}}{(\\alpha \\mathbf{S}+\\beta)}\\)
\n\u0b87\u0ba9\u0baa\u0bcd\u0baa\u0bc6\u0bb0\u0bc1\u0b95\u0bcd\u0b95\u0bae\u0bcd \u0b85\u0ba4\u0bbf\u0b95\u0bae\u0bcd \u0bb5\u0bb0 \u0bb5\u0bbe\u0baf\u0bcd\u0baa\u0bcd\u0baa\u0bc1 \u0b89\u0bb3\u0bcd\u0bb3\u0ba4\u0bbe\u0bb2\u0bcd
\n\u0ba8\u0bbe\u0bae\u0bcd lim R(S) \u0b90\u0b95\u0bcd \u0b95\u0bbe\u0ba3\u0bcd\u0baa\u0bcb\u0bae\u0bcd.
\n\u2234 \\(\\lim _{S \\rightarrow \\infty} R(S)=\\lim _{S \\rightarrow \\infty} \\frac{S}{\\alpha S+\\beta}\\)
\n= \"Samacheer
\n= \\(\\lim _{s \\rightarrow \\infty} \\frac{1}{\\alpha+\\frac{\\beta}{\\mathrm{S}}}\\)
\n[\u2235 S \u2192 \u221e \u0b86\u0b95\u0bc1\u0bae\u0bcd \u0baa\u0bca\u0bb4\u0bc1\u0ba4\u0bc1 \\(\\frac{1}{S}\\) \u2192 0 \u0b86\u0b95\u0bc1\u0bae\u0bcd]
\n= \\(\\frac{1}{\\alpha+0}=\\frac{1}{\\alpha}\\)
\n\u2234 \u0b87\u0ba9\u0baa\u0bcd\u0baa\u0bc6\u0bb0\u0bc1\u0b95\u0bcd\u0b95\u0b9a\u0bcd R(S) \u0b86\u0ba9\u0ba4\u0bc1 \u0b92\u0bb0\u0bc1 \u0bae\u0bbe\u0bb1\u0bbf\u0bb2\u0bbf \u0b8e\u0ba9 \u0ba8\u0bbf\u0bb0\u0bc1\u0baa\u0bbf\u0b95\u0bcd\u0b95\u0baa\u0bcd\u0baa\u0b9f\u0bcd\u0b9f\u0ba4\u0bc1.<\/p>\n

\"Samacheer<\/p>\n

Question 10.
\n\u0b92\u0bb0\u0bc1 \u0ba4\u0bca\u0b9f\u0bcd\u0b9f\u0bbf\u0baf\u0bbf\u0bb2\u0bcd 5000 \u0bb2\u0bbf\u0b9f\u0bcd\u0b9f\u0bb0\u0bcd \u0ba8\u0bb2\u0bcd\u0bb2 \u0ba8\u0bc0\u0bb0\u0bcd \u0b89\u0bb3\u0bcd\u0bb3\u0ba4\u0bc1 \u0b8e\u0ba9\u0bcd\u0b95. \u0b92\u0bb0\u0bc1 \u0bb2\u0bbf\u0b9f\u0bcd\u0b9f\u0bb0\u0bc1\u0b95\u0bcd\u0b95\u0bc1 30 \u0b95\u0bbf \u0b85\u0bb3\u0bb5\u0bc1 \u0b89\u0baa\u0bcd\u0baa\u0bc1 \u0b95\u0bca\u0ba3\u0bcd\u0b9f \u0b89\u0bb5\u0bb0\u0bcd \u0ba8\u0bc0\u0bb0\u0bcd 25 \u0bb2\u0bbf\/\u0ba8\u0bbf\u0bae\u0bbf\u0b9f\u0bae\u0bcd \u0b8e\u0ba9\u0bcd\u0bb1 \u0b85\u0bb3\u0bb5\u0bbf\u0bb2\u0bcd \u0ba4\u0bca\u0b9f\u0bcd\u0b9f\u0bbf\u0baf\u0bbf\u0bb2\u0bcd \u0b9a\u0bc6\u0bb2\u0bc1\u0ba4\u0bcd\u0ba4\u0baa\u0bcd\u0baa\u0b9f\u0bc1\u0b95\u0bbf\u0ba9\u0bcd\u0bb1\u0ba4\u0bc1. 1 \u0ba8\u0bbf\u0bae\u0bbf\u0b9f\u0b99\u0bcd\u0b95\u0bb3\u0bbf\u0bb2\u0bcd \u0b87\u0ba8\u0bcd\u0ba4 \u0b89\u0bb5\u0bb0\u0bcd 30t \u0ba8\u0bc0\u0bb0\u0bbf\u0ba9\u0bcd \u0b85\u0b9f\u0bb0\u0bcd\u0ba4\u0bcd\u0ba4\u0bbf (\u0b95\u0bbf\u0bb0\u0bbe\u0bae\u0bcd \/ \u0bb2\u0bbf\u0b9f\u0bcd\u0b9f\u0bb0\u0bcd) C(t) = \\(\\frac{30 t}{200+t}\\) \u0b8e\u0ba9 \u0ba4\u0bb0\u0baa\u0bcd\u0baa\u0b9f\u0bcd\u0b9f\u0bc1\u0bb3\u0bcd\u0bb3\u0ba4\u0bc1. 1 \u2013 0 \u0b8e\u0ba9\u0bbf\u0bb2\u0bcd \u0b85\u0b9f\u0bb0\u0bcd\u0ba4\u0bcd\u0ba4\u0bbf \u0b8e\u0bb5\u0bcd\u0bb5\u0bbe\u0bb1\u0bc1 \u0bae\u0bbe\u0bb1\u0bc1\u0bae\u0bcd?
\n\u0ba4\u0bc0\u0bb0\u0bcd\u0bb5\u0bc1 :
\nC(t) = \\(\\frac{30 t}{200+t}\\)
\n\\(\\lim _{t \\rightarrow \\infty}\\) C(t) = \\(\\lim _{t \\rightarrow \\infty}\\) \\(\\frac{30 t}{200+t}\\) = \\(\\lim _{t \\rightarrow \\infty}\\) \\(\\frac{30 t}{t\\left(1+\\frac{200}{t}\\right)}\\)
\n= \\(\\lim _{t \\rightarrow \\infty}\\) \\(\\frac{30}{1+\\frac{200}{t}}=\\frac{30}{0+1}\\) = 30
\n[\u2235 t \u2192 \u221e \u0b8e\u0ba9\u0bbf\u0bb2\u0bcd \\(\\frac{1}{t}\\) \u2192 0]
\nt \u2192 \u221e \u0b8e\u0ba9\u0bbf\u0bb2\u0bcd \u0b89\u0bb5\u0bb0\u0bcd\u0ba8\u0bc0\u0bb0\u0bbf\u0ba9\u0bcd \u0b85\u0b9f\u0bb0\u0bcd\u0ba4\u0bcd\u0ba4\u0bbf 30 \u0b95\u0bbf\u0bb0\u0bbe\u0bae\u0bcd \u0b86\u0b95\u0bc1\u0bae\u0bcd.<\/p>\n","protected":false},"excerpt":{"rendered":"

Tamilnadu State Board New Syllabus Samacheer Kalvi 11th Maths Guide Pdf Chapter 9 \u0b95\u0ba3\u0b99\u0bcd\u0b95\u0bb3\u0bcd, \u0ba4\u0bca\u0b9f\u0bb0\u0bcd\u0baa\u0bc1\u0b95\u0bb3\u0bcd \u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd na\u0b9a\u0bbe\u0bb0\u0bcd\u0baa\u0bc1\u0b95\u0bb3\u0bcd Ex 9.3 Textbook Questions and Answers, Notes. TN Board 11th Maths Solutions Chapter 9 \u0b95\u0ba3\u0b99\u0bcd\u0b95\u0bb3\u0bcd, \u0ba4\u0bca\u0b9f\u0bb0\u0bcd\u0baa\u0bc1\u0b95\u0bb3\u0bcd \u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd \u0b9a\u0bbe\u0bb0\u0bcd\u0baa\u0bc1\u0b95\u0bb3\u0bcd Ex 9.3 Question 1. \u0baa\u0bbf\u0ba9\u0bcd\u0bb5\u0bb0\u0bc1\u0bae\u0bcd \u0b9a\u0bbe\u0bb0\u0bcd\u0baa\u0bc1\u0b95\u0bb3\u0bc1\u0b95\u0bcd\u0b95\u0bc1 \u0b87\u0b9f\u0baa\u0bcd\u0baa\u0bc1\u0bb1, \u0bb5\u0bb2\u0baa\u0bcd\u0baa\u0bc1\u0bb1 \u0b8e\u0bb2\u0bcd\u0bb2\u0bc8\u0b95\u0bb3\u0bbf\u0bb2\u0bcd \u0bae\u0ba4\u0bbf\u0baa\u0bcd\u0baa\u0bc8\u0b95\u0bcd \u0b95\u0bbe\u0ba3\u0bcd\u0b95 (a) x = -2-\u0bb2\u0bcd f(x) = (b) x = […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":"","footnotes":""},"categories":[7],"tags":[],"blocksy_meta":"","jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/posts\/50492"}],"collection":[{"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/comments?post=50492"}],"version-history":[{"count":0,"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/posts\/50492\/revisions"}],"wp:attachment":[{"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/media?parent=50492"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/categories?post=50492"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/tags?post=50492"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}