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# evaluate the limit help please :)?

Could someone please help me solve

lim [sqrt(x^2)+a(x)] - [sqrt(x^2+b(x)]

X->(infinity)

Could you please go into some detail with this

= lim ( x→∞ ) (a-b)x / [ √(x²+ax) + √(x²+bx) ] ..... Divide N by x and D by √(x²)

im new at this

oh, numerator and denominator, nvm. Thank you, didnt know what N and D meant

### 1 Answer

- HemantLv 71 decade agoFavorite Answer
L = lim ( x→∞ ) [ √(x²+ax) - √(x²+bx) ] ....... Rationalize

= lim ( x→∞ ) [ √(x²+ax) - √(x²+bx) ] · [ √(x²+ax) + √(x²+bx) ] / [ √(x²+ax) + √(x²+bx) ]

= lim ( x→∞ ) [ (x²+ax) - (x²+bx) ] / [ √(x²+ax) + √(x²+bx) ]

= lim ( x→∞ ) (a-b)x / [ √(x²+ax) + √(x²+bx) ] ..... Divide N by x and D by √(x²)

= lim ( x→∞ ) (a-b) / { √[1+(a/x)] + √[1+(b/x) ] }

= (a-b) / { √(1+0) + √(1+0) }

= (a-b) / 2 ................................... Ans.

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Happy To Help !

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