# 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.

- For what values of x, if any, does #f(x) = 1/(x^2-4x+4) # have vertical asymptotes?
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- How do you evaluate the limit #15/(t^2+5)# as t approaches #1#?
- What are the removable and non-removable discontinuities, if any, of #f(x)=abs(x-9)/ (x-9)#?
- In the limit #lim sqrt(6-3x)=0# as #x->2^-#, how do you find #delta>0# such that whenever #2-delta<x<2#, #sqrt(6-3x)<0.01#?

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