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find value of a and b.?
lim┬(x→∞) [ {(x^2+1)/(x+1)} - ax - b ] = 0
then find (a,b).
2 Answers
- kbLv 77 years agoFavorite Answer
Note that
lim(x→∞) [(x^2+1)/(x+1) - ax - b] = 0
<==> lim(x→∞) [(x^2+1)/(x+1) - (ax+b)*(x+1)/(x+1)] = 0
<==> lim(x→∞) [(x^2+1) - (ax^2 + (a+b)x + b)] / (x+1) = 0
<==> lim(x→∞) [(1-a) x^2 - (a+b)x + (1-b)] / (x+1) = 0.
In order for the limit to be 0, we need 1-a = 0 and -(a+b) = 0
<==> a = 1 and b = -1.
(Now, the degree of the denominator is greater than that of the numerator.)
I hope this helps!
- Anonymous7 years ago
lim ( x -- > inf ) [ ( x^2 + 1 ) - ( ax + b ) ( x + 1 ) ] / ( x + 1 ) = 0
lim ( x -- > inf ) [ ( x^2 + 1 - ( ax^2 + ( a + b )x + b ) ) / ( x + 1 ) ] = 0
lim ( x -- > inf ) [ 2 ( 1 - a )x - ( a + b ) ] = 0
the only way this can be zero is if 1 - a = 0
so a = 1
but then a + b must also be 0; so 1 + b = 0
b = - 1
Source(s): my brain
