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E v a l u a t e space limit as x rightwards arrow 0 of open parentheses fraction numerator 1 plus 7 x over denominator 1 minus 9 x end fraction close parentheses to the power of 1 over x end exponent

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Asked by Topperlearning User 16th November 2016, 4:27 AM
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limit as x rightwards arrow 0 of open parentheses fraction numerator 1 plus 7 x over denominator 1 minus 9 x end fraction close parentheses to the power of 1 over x end exponent
equals e to the power of limit as x rightwards arrow 0 of 1 over x log open parentheses fraction numerator 1 plus 7 x over denominator 1 minus 9 x end fraction close parentheses end exponent
limit as x rightwards arrow 0 of 1 over x log open parentheses fraction numerator 1 plus 7 x over denominator 1 minus 9 x end fraction close parentheses
equals limit as x rightwards arrow 0 of fraction numerator 7 log left parenthesis 1 plus 7 x right parenthesis over denominator 7 x end fraction minus limit as x rightwards arrow 0 of fraction numerator negative 9 log left parenthesis 1 minus 9 x right parenthesis over denominator negative 9 x end fraction
equals 7 plus 9 equals 16
e to the power of limit as x rightwards arrow 0 of 1 over x log open parentheses fraction numerator 1 plus 7 x over denominator 1 minus 9 x end fraction close parentheses end exponent equals e to the power of 16

Answered by Expert 16th November 2016, 6:27 AM
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