How do you determine the limit of #(x+4)/(x-4)# as x approaches 4+?

Answer 1

#lim_(x->4^+) (x+4)/(x-4) = oo#

#lim_(x->4^+) (x+4) = 8#
#therefore 8lim_(x->4^+) 1/(x-4) #
As #lim_(x->4^+) (x-4) = 0# and all points on the approach from the right are greater than zero, we have:
#lim_(x->4^+) 1/(x-4) = oo#
#implies lim_(x->4^+) (x+4)/(x-4) = oo#
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Answer 2

To determine the limit of (x+4)/(x-4) as x approaches 4+, we substitute the value 4 into the expression. This gives us (4+4)/(4-4), which simplifies to 8/0. Since division by zero is undefined, 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.

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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