Example 2 - Find limits (i) lim x->1 [x2 + 1 / x + 100] - Examples

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  1. Class 11
  2. Important Question for exams Class 11
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Example , 2 Find the limits: (i) lim x 1 x2 + 1 x + 100 lim x 1 x2 + 1 x + 100 Putting x = 1 = 1 2 + 1 1 + 100 = 1 + 1 101 = Example, 2 Find the limits: (ii) lim x 2 x3 4x2+4x x2 4 lim x 2 x3 4x2 + 4x x2 4 = lim x 2 2 4 + 4 2 (2) 2 = lim x 2 2 2 2 + 4 2 ( + 2) = lim x 2 2 2 ( 2) 2 ( + 2) = lim x 2 2 ( 2) 2 ( + 2) = + Putting x = 2 = 2 (2 2) 2 + 2 = 2 (0) 4 = 0 4 = 0 Example, 2 Find the limits: (iii) lim x 2 x2 4 x3 4x2 + 4x lim x 2 x2 4 x3 4x2 + 4x = lim x 2 x2 2 2 x(x2 4x + 4) = lim x 2 2 ( + 2) x(x x 2 2 x 2 ) = lim x 2 2 ( + 2) x 2 x 2 = + Putting x = 2 = 2 + 2 2 2 2 = 2 + 2 2 2 2 = 4 2(0) = = Which is not defined Example 2 Find the limits: (iv) lim x 2 x3 2 2 x2 5x+6 lim x 2 x3 2 2 x2 5x + 6 = lim x 2 x2 x 2 2 3 2 + 6 = lim x 2 x2 x 2 x x 3 2 x 3 = lim x 2 x2 x 2 x 2 x 3 = Putting x = 2 = 2 2 2 3 = 2 2 2 3 = 4 1 = 4 Example 2 Find the limits: (v) lim x 1 x 2 x2 x 1 3 3 2+2 lim x 1 x 2 x2 x 1 3 3 2 + 2 = lim x 1 x 2 x (x 1) 1 ( 2 3 + 2) = lim x 1 x 2 x (x 1) 1 ( 2 2 + 2) = lim x 1 x 2 x (x 1) 1 ( 2 1 2 ) = lim x 1 x 2 x (x 1) 1 1 ( 2) = lim x 1 x 2 2 1 1 ( 2) = lim x 1 x 2 2 1 1 ( 2) = lim x 1 x 2 2 1 1 ( 2) = lim x 1 2 + 2 2 2 2 1 1 ( 2) = lim x 1 2 + 4 4 1 1 ( 2) = ( ) Putting x = 1 = 1 2 4 1 + 3 1 1 1 (1 2) = Since it is 0 0 form we can simplify = lim x 1 2 4 3 1 ( 2) = lim x 1 2 4 3 1 ( 2) = lim x 1 2 3 + 3 1 ( 2) = lim x 1 3 1( 3) 1 ( 2) = lim x 1 1 ( 3) 1 ( 2) = ( ) Putting x = 1 = 1 3 1 (1 2) = 1 3 1( 1) = 2 1 = 2

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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.