{"id":3127,"date":"2023-12-03T11:45:07","date_gmt":"2023-12-03T06:15:07","guid":{"rendered":"https:\/\/wordpress-505192-1602719.cloudwaysapps.com\/?p=3127"},"modified":"2023-12-04T12:54:44","modified_gmt":"2023-12-04T07:24:44","slug":"samacheer-kalvi-11th-maths-solutions-chapter-9-ex-9-1","status":"publish","type":"post","link":"https:\/\/samacheerguru.com\/samacheer-kalvi-11th-maths-solutions-chapter-9-ex-9-1\/","title":{"rendered":"Samacheer Kalvi 11th Maths Solutions Chapter 9 Limits and Continuity Ex 9.1"},"content":{"rendered":"

You can Download Samacheer Kalvi 11th Maths Book Solutions<\/a> Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.<\/p>\n

Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 9 Limits and Continuity Ex 9.1<\/h2>\n

In problems 1-6, complete the table using calculate and use the result to estimate the limit.
\nQuestion 1.
\n\"Samacheer
\nSolution:
\n\"Samacheer<\/p>\n

Question 2.
\n\"Samacheer
\nSolution:
\n\"Samacheer
\n\u2234 Limit is 0.25<\/p>\n

Question 3.
\n\"Samacheer
\nSolution:
\n\"Samacheer
\n\u2234 Limit is 0.288<\/p>\n

Question 4.
\n\"Samacheer
\nSolution:
\n\"Samacheer
\n\u2234 Limit is -0.25<\/p>\n

\"Samacheer<\/p>\n

Question 5.
\n\"Samacheer
\nSolution:
\n\"Samacheer
\n\u2234 Limit is 1<\/p>\n

Question 6.
\n\"Samacheer
\nSolution:
\n\"Samacheer
\n\u2234 Limit is 0<\/p>\n

In exercise problems 7-15, use the graph to find the limits (if it exists). If the limit does not exist, explain why?
\nQuestion 7.
\n\\(\\lim _{x \\rightarrow 3}\\)(4 – x)
\nSolution:
\n\"Samacheer
\nLimit exist and is equal to 1<\/p>\n

Question 8.
\n\\(\\lim _{x \\rightarrow 1}\\)(x2<\/sup> + 2)
\nSolution:
\n\"Samacheer
\nLimit exist and is equal to = 3<\/p>\n

Question 9.
\n\"Samacheer
\nSolution:
\n\"Samacheer<\/p>\n

Question 10.
\n\"Samacheer
\nSolution:
\n\"Samacheer<\/p>\n

Question 11.
\n\"Samacheer
\nSolution:
\n\"Samacheer
\nLimit does not exist<\/p>\n

\"Samacheer<\/p>\n

Question 12.
\n\"Samacheer
\nSolution:
\nWhen x \u2192 5, (x – 5) = -(x – 5)
\n\u2234 \\(\\lim _{x \\rightarrow 5^{-}} \\frac{-(x-5)}{(x-5)}\\) = -1
\nWhen x \u2192 5+<\/sup>, (x – 5) = (x – 5)
\n\"Samacheer
\n\"Samacheer<\/p>\n

Question 13.
\n\\(\\lim _{x \\rightarrow 1}\\) sin(\u03c0x)
\nSolution:
\n\"Samacheer
\n\"Samacheer<\/p>\n

Question 14.
\n\\(\\lim _{x \\rightarrow 0}\\) (sec x)
\nSolution:
\n\"Samacheer<\/p>\n

Question 15.
\n\\(\\lim _{x \\rightarrow \\frac{\\pi}{2}}\\) tan x
\nSolution:
\n\"Samacheer
\nLimit does not exist<\/p>\n

Sketch the graph of f, then identify the values of x0<\/sub> for which \\(\\lim _{x \\rightarrow x_{0}}\\) f(x) exists.
\nQuestion 16.
\n\"Samacheer
\nSolution:
\n\"Samacheer<\/p>\n

Question 17.
\n\"Samacheer
\nSolution:
\n\"Samacheer
\nLimit exists except at x0<\/sub> = \u03c0<\/p>\n

\"Samacheer<\/p>\n

Question 18.
\nSketch the graph of a function f that satisfies the given values:
\n\"Samacheer
\nSolution:
\n\"Samacheer<\/p>\n

Question 19.
\nWrite a brief description of the meaning of the notation \\(\\lim _{x \\rightarrow 8}\\) f(x) = 25
\nSolution:
\n\"Samacheer<\/p>\n

Question 20.
\nIf f(2) = 4, can you conclude anything about the limit of f(x) as x approaches 2?
\nSolution:
\nNo, f(x) = 4, It is the value of the function at x = 2
\nThis limit doesn’t exists at x = 2
\nSince f(2) = 4
\nIt need not imply that \\(\\lim _{x \\rightarrow 2^{-}} f(x)=\\lim _{x \\rightarrow 2^{+}} f(x)\\)
\n\u2234 we cannot conclude at x = 2<\/p>\n

Question 21.
\nIf the limit of f(x) as z approaches 2 is 4, can you conclude anything about f(2)?
\nExplain reasoning.
\nSolution:
\n\\(\\lim _{x \\rightarrow 2}\\) f(x) 4 , \\(\\lim _{x \\rightarrow 2^{-}}\\) f(x) = \\(\\lim _{x \\rightarrow 2^{+}}\\) f(x) = 4
\nWhen x approaches 2 from the left or from the right f(x) approaches 4.
\nGiven that \\(\\lim _{x \\rightarrow 2^{-}}\\) f(x) = \\(\\lim _{x \\rightarrow 2^{+}}\\) f(x) = 4
\nThe existence or non existence at x =2 has no leaving on the existence of the limit of f(x) as x approaches to 2.
\n\u2234 We cannot conclude the value of f(2)<\/p>\n

Question 22.
\nEvaluate: \\(\\lim _{x \\rightarrow 3} \\frac{x^{2}-9}{x-3}\\) if it exists by finding f(3–<\/sup>) and f(3+<\/sup>).
\nSolution:
\n\"Samacheer
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 23.
\nVerify the existence of \"Samacheer
\nSolution:
\n\"Samacheer
\nLimit does not exist<\/p>\n

Samacheer Kalvi 11th Maths Solutions Chapter 9 Limits and Continuity Ex 9.1 Additional Questions<\/h3>\n

Question 1.
\nSuppose \"Samacheer. What are possible values of a and b?
\nSolution:
\n\"Samacheer<\/p>\n

Question 2.
\n\"Samacheer
\nSolution:
\nWe have,
\n\"Samacheer<\/p>\n

Question 3.
\n\"Samacheer
\nSolution:
\nWe have,
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 4.
\n\"Samacheer
\nSolution:
\n\"Samacheer
\n\"Samacheer<\/p>\n

Question 5.
\nLet a1<\/sub>, a2<\/sub> …………… an<\/sub> be fixed real numbers such that f(x) = (x – a1<\/sub>) , (x – a2<\/sub>), ………. (x – an<\/sub>) what \\(\\lim _{x \\rightarrow a}\\) f(x) For a \u2260 a1<\/sub>, a2<\/sub>, ………… an<\/sub> compute \\(\\lim _{x \\rightarrow a}\\) f(x)
\nSolution:
\nWe have,
\n\"Samacheer<\/p>\n","protected":false},"excerpt":{"rendered":"

You can Download Samacheer Kalvi 11th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations. Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 9 Limits and Continuity Ex 9.1 In problems 1-6, complete the table using calculate and use the result to estimate […]<\/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\/3127"}],"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=3127"}],"version-history":[{"count":1,"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/posts\/3127\/revisions"}],"predecessor-version":[{"id":55179,"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/posts\/3127\/revisions\/55179"}],"wp:attachment":[{"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/media?parent=3127"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/categories?post=3127"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samacheerguru.com\/wp-json\/wp\/v2\/tags?post=3127"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}