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F i n d space t h e space v a l u e space o f space limit as x rightwards arrow 0 of left parenthesis f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis right parenthesis space w h e r e
space f left parenthesis x right parenthesis equals x squared plus 2 x plus 3 space a n d space g left parenthesis x right parenthesis equals fraction numerator 1 over denominator 1 plus x end fraction

Please provide solution to this question

Asked by Topperlearning User 16th November 2016, 1:18 AM
Answered by Expert
Answer:

limit as x rightwards arrow 0 of left square bracket f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis right square bracket equals limit as x rightwards arrow 0 of f left parenthesis x right parenthesis plus limit as x rightwards arrow 0 of g left parenthesis x right parenthesis
limit as x rightwards arrow 0 of space f left parenthesis x right parenthesis
equals limit as x rightwards arrow 0 of left parenthesis x squared plus 2 x plus 3 right parenthesis
equals limit as x rightwards arrow 0 of x squared plus limit as x rightwards arrow 0 of 2 x plus limit as x rightwards arrow 0 of 3
equals 0 plus 0 plus 3 equals 3

limit as x rightwards arrow 0 of space g left parenthesis x right parenthesis
equals limit as x rightwards arrow 0 of fraction numerator 1 over denominator 1 plus x end fraction
equals fraction numerator 1 over denominator limit as x rightwards arrow 0 of left parenthesis 1 plus x right parenthesis end fraction
equals 1
S o space limit as x rightwards arrow 0 of left square bracket f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis right square bracket equals 3 plus 1 equals 4

Answered by Expert 16th November 2016, 3:18 AM
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