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Ex 5.1, 29 - Find k. f(x) = {kx + 1, 3x - 5 is continuous at x=5 - Checking continuity using LHL and RHL

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  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise
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Ex 5.1, 29 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‰ค5๏ทฎ3๐‘ฅโˆ’5, ๐‘–๐‘“ ๐‘ฅ>5๏ทฏ๏ทฏ at x = 5 Given, ๐‘“ ๐‘ฅ๏ทฏ= ๐‘˜๐‘ฅ+1, ๐‘–๐‘“ ๐‘ฅโ‰ค5๏ทฎ3๐‘ฅโˆ’5, ๐‘–๐‘“ ๐‘ฅ>5๏ทฏ๏ทฏ Given function is continuous at ๐‘ฅ =5 if L.H.L = R.H.L = ๐‘“(5) i.e. lim๏ทฎxโ†’ 5๏ทฎโˆ’๏ทฏ๏ทฏ ๐‘“ ๐‘ฅ๏ทฏ= lim๏ทฎxโ†’ 5๏ทฎ+๏ทฏ๏ทฏ ๐‘“(๐‘ฅ)= ๐‘“(5) Now, L.H.L = R.H.L โ‡’ 5๐‘˜+1=10 โ‡’ 5๐‘˜=10โˆ’1 โ‡’ 5๐‘˜=9 โ‡’ ๐‘˜= 9๏ทฎ5๏ทฏ Hence ๐’Œ= ๐Ÿ—๏ทฎ๐Ÿ“๏ทฏ

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