Last updated at March 12, 2021 by Teachoo
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Example 12 Discuss the continuity of the function defined by ๐(๐ฅ)={โ(& ๐ฅ+2, ๐๐ ๐ฅ<0@&โ๐ฅ+2, ๐๐ ๐ฅ>0)โค ๐(๐ฅ)={โ(& ๐ฅ+2, ๐๐ ๐ฅ<0@&โ๐ฅ+2, ๐๐ ๐ฅ>0)โค Here, function is not defined for x = 0 So, we do not check continuity there We check continuity for different values of x When x < 0 When x > 0 Case 1 : When x < 0 For x < 0, f(x) = x + 2 Since this a polynomial It is continuous โด f(x) is continuous for x < 0 Case 2 : When x > 0 For x > 0, f(x) = โx + 2 Since this a polynomial It is continuous โด f(x) is continuous for x > 0 Hence, ๐ is continuous for all Real points except 0. Thus, ๐ is continuous for ๐ โ๐โ{๐}
Checking continuity using LHL and RHL
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Example 11
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Example 15
Checking continuity using LHL and RHL
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