What is the answer for this question?

Asked by dineshchem108 | 16th Apr, 2019, 10:58: PM

Expert Answer:

begin mathsize 16px style limit as straight x rightwards arrow 0 of space fraction numerator square root of straight x squared plus 1 end root minus 1 over denominator square root of straight x squared plus 9 end root minus 3 end fraction
equals limit as straight x rightwards arrow 0 of space fraction numerator square root of straight x squared plus 1 end root minus 1 over denominator square root of straight x squared plus 9 end root minus 3 end fraction cross times fraction numerator square root of straight x squared plus 9 end root plus 3 over denominator square root of straight x squared plus 9 end root plus 3 end fraction
equals limit as straight x rightwards arrow 0 of space fraction numerator open parentheses square root of straight x squared plus 1 end root minus 1 close parentheses open parentheses square root of straight x squared plus 9 end root plus 3 close parentheses over denominator straight x squared plus 9 minus 9 end fraction
equals limit as straight x rightwards arrow 0 of space fraction numerator open parentheses square root of straight x squared plus 1 end root minus 1 close parentheses open parentheses square root of straight x squared plus 9 end root plus 3 close parentheses over denominator straight x squared end fraction cross times fraction numerator square root of straight x squared plus 1 end root plus 1 over denominator square root of straight x squared plus 1 end root plus 1 end fraction
equals limit as straight x rightwards arrow 0 of space fraction numerator open parentheses straight x squared plus 1 minus 1 close parentheses open parentheses square root of straight x squared plus 9 end root plus 3 close parentheses over denominator straight x squared open parentheses square root of straight x squared plus 1 end root plus 1 close parentheses end fraction
equals equals limit as straight x rightwards arrow 0 of space fraction numerator straight x squared open parentheses square root of straight x squared plus 9 end root plus 3 close parentheses over denominator straight x squared open parentheses square root of straight x squared plus 1 end root plus 1 close parentheses end fraction
equals limit as straight x rightwards arrow 0 of space fraction numerator square root of straight x squared plus 9 end root plus 3 over denominator square root of straight x squared plus 1 end root plus 1 end fraction
equals fraction numerator 3 plus 3 over denominator 1 plus 1 end fraction
equals 3 end style

Answered by Sneha shidid | 17th Apr, 2019, 09:13: AM