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Limits And Derivatives

Question
CBSEENMA11013112
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Evaluate the following :

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Solution
space space space space space limit as space space straight x rightwards arrow negative 1 of left parenthesis 1 plus straight x plus straight x squared plus...... space plus space straight x squared right parenthesis space equals stack lim space space left parenthesis 1 right parenthesis with straight x rightwards arrow negative 1 below plus limit as straight x rightwards arrow negative 1 of left parenthesis straight x right parenthesis space plus space limit as straight x rightwards arrow negative 1 of straight x squared plus space...... plus space limit as straight x rightwards arrow negative 1 of straight x to the power of 12
        = 1 + (-1) + (-1)2 + .... + (-1)12 = 1 + (-1) + 1 + ..... + 1 = 1

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