Last updated at March 12, 2021 by
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Example 12 Discuss the continuity of the function defined by π(π₯)={β(& π₯+2, ππ π₯<0@&βπ₯+2, ππ π₯>0)β€ π(π₯)={β(& π₯+2, ππ π₯<0@&βπ₯+2, ππ π₯>0)β€ 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 β΄ f(x) is continuous for x < 0 Case 2 : When x > 0 For x > 0, f(x) = βx + 2 Since this a polynomial It is continuous β΄ f(x) is continuous for x > 0 Hence, π is continuous for all Real points except 0. Thus, π is continuous for π βπβ{π}
Checking continuity using LHL and RHL
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Checking continuity using LHL and RHL
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