Ex 5.1, 28 - Find k so that f(x) = { kx + 1, cos x at x = pi - Ex 5.1

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  1. Class 12
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Ex 5.1, 28 Find the values of k so that the function f is continuous at the indicated point ๐‘“ ๐‘ฅ๏ทฏ= ๐‘˜๐‘ฅ+1 , ๐‘–๐‘“ ๐‘ฅโ‰ค๐œ‹๏ทฎ cos๏ทฎ๐‘ฅ, ๏ทฏ ๐‘–๐‘“ ๐‘ฅ>๐œ‹๏ทฏ๏ทฏ at x = ๐œ‹ Given, ๐‘“ ๐‘ฅ๏ทฏ= ๐‘˜๐‘ฅ+1 , ๐‘–๐‘“ ๐‘ฅโ‰ค๐œ‹๏ทฎ cos๏ทฎ๐‘ฅ, ๏ทฏ ๐‘–๐‘“ ๐‘ฅ>๐œ‹๏ทฏ๏ทฏ at x = ๐œ‹ Given that function is continuous at ๐‘ฅ =๐œ‹ ๐‘“ is continuous at ๐‘ฅ =๐œ‹ if L.H.L = R.H.L = ๐‘“(๐œ‹) i.e. lim๏ทฎxโ†’ ๐œ‹๏ทฎโˆ’๏ทฏ๏ทฏ ๐‘“ ๐‘ฅ๏ทฏ= lim๏ทฎxโ†’ ๐œ‹๏ทฎ+๏ทฏ๏ทฏ ๐‘“(๐‘ฅ)= ๐‘“(๐œ‹) Since L.H.L = R.H.L โ‡’ ๐‘˜๐œ‹+1=โˆ’1 โ‡’ ๐‘˜๐œ‹=โˆ’2 Hence, ๐’Œ= โˆ’๐Ÿ๏ทฎ๐…๏ทฏ

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.