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Continuity And Differentiability

Question
CBSEENMA12034423
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Examine the continuity of the function f(x) = 2x2 –1 at.x = 3

Solution

Here
      straight f left parenthesis straight x right parenthesis equals 2 straight x squared minus 1 Lt with straight x rightwards arrow 3 below space straight f left parenthesis straight x right parenthesis equals Lt with straight x rightwards arrow 3 below space left parenthesis 2 straight x squared minus 1 right parenthesis equals 2 left parenthesis 3 right parenthesis squared minus 1 equals 2 left parenthesis 9 right parenthesis minus 1 equals 18 minus 1 equals 17 Now space straight f space is space defined space at space straight x equals 3 and space space space space straight f left parenthesis straight x right parenthesis equals 2 left parenthesis 3 right parenthesis squared minus 1 equals 2 left parenthesis 9 right parenthesis minus 1 equals 18 minus 1 equals 17 therefore Lt with straight x rightwards arrow 3 below space space space straight f left parenthesis straight x right parenthesis equals straight f left parenthesis 3 right parenthesis equals 17 therefore space straight f space is space continous space at space straight x equals 3.

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