How do you find the limit of #(x+3)/(x-3)# as x approaches 3+?

Answer 1

Paisley Johnson

As #xrarr3^+#, the numerator #x+3# #rarr 6#.

The denominator #x-3# #rarr 0#.

So the fraction is either increasing without bound (#rarroo#) or decreasing without bound (#rarr -oo#)

As #xrarr3^+#, we know that #x > 3# so #x-3 > 3-3 =0#. That is

As #xrarr3^+#, #x-3# #rarr 0# through positive values.

(As #xrarr3^+#, #x-3# #rarr 0^+# or #lim_(xrarr3^+)(x-3) = 0^+#)

The fraction is growing without bound because the denominator will go to 0 and the numerator will go to a positive through positives.

#lim_(xrarr3^+)(x+3)/(x-3) = oo#

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Answer 2

Charles Anctil

To find the limit of (x+3)/(x-3) as x approaches 3+, we substitute the value 3 into the expression. However, this results in an undefined expression since division by zero is not defined. Therefore, the limit does not exist.

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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.