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How do you find the limit #lim 3^t-2^t# as #t->oo#?

Answer 1

There is no limit as #t->oo#, the equation will continue to approach #oo# as #t->oo#

Not much maths is involved in this.

You know that you are taking one exponential growth from another. However, the smaller one is being taken away from the bigger one. Also, the gap between #3^t# and #2^t# will continue to get greater and greater.

The equation would plot the value for this gap against #t#, and as one is growing faster than the other, the line will move further and further away from 0.

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Answer 2

Paisley Johnson

To find the limit of lim 3^t - 2^t as t approaches infinity, we can use the concept of exponential growth. As t becomes larger and larger, the term 3^t will grow much faster than 2^t. Therefore, the limit of the expression as t approaches infinity is positive 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.

How do you find the limit #lim 3^t-2^t# as #t-&gt;oo#?

How do you find the limit #lim 3^t-2^t# as #t->oo#?