If the function f (x) = {(x 2   - 1)/(x - 1) when x ≠ 1,  k when x = 1 } is given to be continuous at x = 1, then the value of k is ________ 

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Transcript

Question 12 If the function 𝑓(π‘₯)={(π‘₯^2 βˆ’ 1)/(π‘₯ βˆ’ 1) π‘€β„Žπ‘’π‘› π‘₯β‰ 1 @π‘˜ π‘€β„Žπ‘’π‘› π‘₯=1 )─is given to be continuous at x = 1, then the value of k is ________ Since f(x) is continuous at x = 1, then lim┬(xβ†’1) 𝑓(π‘₯)=𝑓(1) lim┬(xβ†’1) ((π‘₯^2 βˆ’ 1)/(π‘₯ βˆ’ 1)) =π‘˜ lim┬(xβ†’1) (((π‘₯ βˆ’ 1)(π‘₯ + 1))/(π‘₯ βˆ’ 1)) =π‘˜ lim┬(xβ†’1) (π‘₯+1) =π‘˜ 1 + 1 = k 2 = k k = 2 Therefore, k = 2

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.