How do you evaluate the limit #x-sqrt(x^2+x)# as x approaches #oo#?

Answer 1

#= - 1/2#

#lim_(x to oo) x-sqrt(x^2+x)#
#= lim_(x to oo) x-x (1+1/x)^(1/2)#

and Binomial expansion

#= lim_(x to oo) x-x (1+1/2 *1/x + O (1/x^2) )#
#= lim_(x to oo) x- x - 1/2 + O(1/x)#
#= - 1/2#
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Answer 2

The limit of x - sqrt(x^2 + x) as x approaches infinity is -1/2.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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