What is the answer for this question?

Asked by dineshchem108 | 1st May, 2019, 07:09: PM

Expert Answer:

begin mathsize 16px style limit as straight x rightwards arrow 2 of space fraction numerator 2 to the power of straight x plus 2 to the power of 3 minus straight x end exponent minus 6 over denominator square root of 2 to the power of negative straight x end exponent end root minus 2 to the power of 1 minus straight x end exponent end fraction
equals limit as straight x rightwards arrow 2 of space fraction numerator 2 to the power of straight x plus begin display style 8 over 2 to the power of straight x end style minus 6 over denominator square root of begin display style 1 over 2 to the power of straight x end style end root minus begin display style 2 over 2 to the power of straight x end style end fraction
equals limit as straight x rightwards arrow 2 of space fraction numerator begin display style fraction numerator open parentheses 2 to the power of straight x close parentheses squared plus begin display style 8 end style minus 6 cross times 2 to the power of straight x over denominator 2 to the power of straight x end fraction end style over denominator begin display style 1 over 2 to the power of straight x end style open parentheses square root of 2 to the power of straight x end root minus 2 close parentheses end fraction
equals limit as straight x rightwards arrow 2 of space fraction numerator begin display style open parentheses 2 to the power of straight x close parentheses squared plus 8 minus 6 cross times 2 to the power of straight x end style over denominator begin display style square root of 2 to the power of straight x end root minus 2 end style end fraction
Put space 2 to the power of straight x equals straight t space
when space straight x rightwards arrow 2 space then space straight t rightwards arrow 4
equals limit as straight t rightwards arrow 4 of space fraction numerator begin display style straight t squared plus 8 minus 6 straight t end style over denominator begin display style square root of straight t minus 2 end style end fraction
equals limit as straight t rightwards arrow 4 of space fraction numerator begin display style straight t squared plus 8 minus 6 straight t end style over denominator begin display style square root of straight t minus 2 end style end fraction cross times fraction numerator square root of straight t plus 2 over denominator square root of straight t plus 2 end fraction
equals limit as straight t rightwards arrow 4 of space fraction numerator begin display style left parenthesis straight t minus 4 right parenthesis left parenthesis straight t minus 2 right parenthesis end style over denominator begin display style straight t minus 4 end style end fraction cross times open parentheses square root of straight t plus 2 space close parentheses
equals limit as straight t rightwards arrow 4 of space left parenthesis straight t minus 2 right parenthesis cross times open parentheses square root of straight t plus 2 space close parentheses space space space space space space space space space space space space space space space space space space space space straight t rightwards arrow 4 space rightwards double arrow straight t minus 4 not equal to 0
equals 2 cross times 4
equals 8

end style

Answered by Sneha shidid | 2nd May, 2019, 09:30: AM