{"id":23862,"date":"2025-01-06T10:00:11","date_gmt":"2025-01-06T04:30:11","guid":{"rendered":"https:\/\/samacheerkalvi.guide\/?p=23862"},"modified":"2025-01-07T10:09:47","modified_gmt":"2025-01-07T04:39:47","slug":"samacheer-kalvi-11th-maths-guide-chapter-5-ex-5-4","status":"publish","type":"post","link":"https:\/\/samacheerkalvi.guide\/samacheer-kalvi-11th-maths-guide-chapter-5-ex-5-4\/","title":{"rendered":"Samacheer Kalvi 11th Maths Guide Chapter 5 Binomial Theorem, Sequences and Series Ex 5.4"},"content":{"rendered":"

Tamilnadu State Board New Syllabus\u00a0Samacheer Kalvi 11th Maths Guide<\/a> Pdf Chapter 5 Binomial Theorem, Sequences and Series Ex 5.4 Text Book Back Questions and Answers, Notes.<\/p>\n

Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 5 Binomial Theorem, Sequences and Series Ex 5.4<\/h2>\n

Having trouble working out with the Binomial theorem? You’ve come to the right place, our Binomial Expansion Calculator<\/a> is here to save the day for you.<\/p>\n

Question 1.
\nExpand the following in ascending powers of x and find the condition on x for which the binomial expansion is valid.
\n(i) \\(\\frac{1}{5+x}\\)
\nAnswer:
\n\"Samacheer
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

(ii) \\(\\frac{2}{(3+4 x)^{2}}\\)
\nAnswer:
\n\"Samacheer<\/p>\n

(iii) (5 + x2<\/sup>)2\/3<\/sup>
\nAnswer:
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

(iv) \\((x+2)^{-\\frac{2}{3}}\\)
\nAnswer:
\n\"Samacheer
\n\"Samacheer<\/p>\n

Expanding binomials calculator<\/a> is a free online tool that displays the expansion of the given binomial term.<\/p>\n

Question 2.
\nFind \\(\\sqrt[3]{1001}\\) approximately. (two decimal places)
\nAnswer:
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 3.
\nProve that \\(\\sqrt[3]{x^{3}+6}-\\sqrt[3]{x^{3}+3}\\) is approximately equal to \\(\\frac{1}{x^{2}}\\) when x is sufficiently large.
\nAnswer:
\n\"Samacheer
\n\"Samacheer
\n\"Samacheer
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 4.
\nProve that \\(\\sqrt{\\frac{1-x}{1+x}}\\) is approximately equal to 1 – x + \\(\\frac{x^{2}}{2}\\) when x is very small.
\nAnswer:
\n\"Samacheer
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 5.
\nWrite the first 6 terms of the exponential series
\n(i) e5x<\/sup>
\nAnswer:
\n\"Samacheer<\/p>\n

(ii) e-2x<\/sup>
\nAnswer:
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

(iii) ex\/2<\/sup>
\nAnswer:
\n\"Samacheer
\n\"Samacheer<\/p>\n

Question 6.
\nWrite the first 4 terms of the logarithmic series.
\n(i) log (1 + 4x)
\n(ii) log (1 – 2x)
\n(iii) log \\(\\left(\\frac{1+3 x}{1-3 x}\\right)\\)
\n(iv) log \\(\\left(\\frac{1-2 x}{1+2 x}\\right)\\)
\nFind the intervals on which the expansions are valid.
\nAnswer:
\n(i) log ( 1 + 4x )
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

(ii) log (1 – 2x)
\n\"Samacheer<\/p>\n

(iii) log \\(\\left(\\frac{1+3 x}{1-3 x}\\right)\\)
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

(iv) log \\(\\left(\\frac{1-2 x}{1+2 x}\\right)\\)
\n\"Samacheer
\n\"Samacheer<\/p>\n

Question 7.
\n\"Samacheer
\nAnswer:
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 8.
\n\"Samacheer
\nAnswer:
\n\"Samacheer
\n\"Samacheer
\n\"Samacheer
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 9.
\nFind the coefficient of x4<\/sup> in the expansion of \\(\\frac{3-4 x+x^{2}}{e^{2 x}}\\)
\nAnswer:
\n\"Samacheer<\/p>\n

\"Samacheer<\/p>\n

Question 10.
\nFind the value of \"Samacheer
\nAnswer:
\n\"Samacheer
\n\"Samacheer<\/p>\n","protected":false},"excerpt":{"rendered":"

Tamilnadu State Board New Syllabus\u00a0Samacheer Kalvi 11th Maths Guide Pdf Chapter 5 Binomial Theorem, Sequences and Series Ex 5.4 Text Book Back Questions and Answers, Notes. Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 5 Binomial Theorem, Sequences and Series Ex 5.4 Having trouble working out with the Binomial theorem? You’ve come to the right place, …<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false},"version":2}},"categories":[6],"tags":[],"class_list":["post-23862","post","type-post","status-publish","format-standard","hentry","category-class-11"],"jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/23862"}],"collection":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/comments?post=23862"}],"version-history":[{"count":2,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/23862\/revisions"}],"predecessor-version":[{"id":39664,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/23862\/revisions\/39664"}],"wp:attachment":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/media?parent=23862"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/categories?post=23862"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/tags?post=23862"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}