# What is #lim_(xrarr0) ( 9/x-(9x)/(x^2+x))#?

It is

#lim_(xrarr0) ( 9/x-(9x)/(x^2+x))=>lim_(xrarr0) ( 9/x-(9x)/(x(x+1)))=> lim_(xrarr0)(9/x-9/(x+1))=lim_(xrarr0)(9/(x(x+1)))=oo#

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The limit of (9/x - (9x)/(x^2+x)) as x approaches 0 is 9.

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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.

- How do you find the limit of #[(pi)tan(x)-(2x)/(cos(x))]# as x approaches pi/2?
- What is the vertical asymptote for #y=9/(x-1)#?
- How do you find the limit #(cosx-1)/sinx# as #x->0#?
- How do you determine the limit of #cos(x) # as n approaches #oo#?
- How do you evaluate the limit #root3((x-3)/(5-x))# as x approaches #-oo#?

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