How do you evaluate #(2^x-3^-x)/(2^x+3^-x)# as x approaches infinity?

Answer 1

#lim_{x->oo}(2^x-3^-x)/(2^x+3^-x) =1#

#(2^x-3^-x)/(2^x+3^-x) =(1-6^{-x})/(1+6^{-x})#
#lim_{x->oo}(2^x-3^-x)/(2^x+3^-x) = (1-lim_{x->oo}6^{-x})/(1+lim_{x->oo}6^{-x}) = 1#
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Answer 2

As x approaches infinity, the expression (2^x-3^-x)/(2^x+3^-x) can be evaluated by considering the dominant terms in the numerator and denominator. In this case, the dominant terms are 2^x in the numerator and 2^x in the denominator.

Since the exponent x approaches infinity, the term 3^-x becomes negligible compared to 2^x. Therefore, we can simplify the expression by ignoring the term 3^-x in both the numerator and denominator.

This simplification leads to (2^x)/(2^x), which equals 1.

Therefore, as x approaches infinity, the value of (2^x-3^-x)/(2^x+3^-x) approaches 1.

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Answer 3

As x approaches infinity, the expression (2^x - 3^(-x)) / (2^x + 3^(-x)) can be simplified by considering the dominant terms in the numerator and denominator. Since 2^x grows much faster than 3^(-x) as x approaches infinity, the terms involving 3^(-x) become negligible compared to those involving 2^x. Therefore, the expression simplifies to 1 in the limit as x approaches infinity.

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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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