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How do you find the limit of # [-1/5(1-(1/x)^(4/5)]# as x approaches infinity?

Answer 1

Remember that #lim_(x->oo)1/x=0#. Answer: #-1/5#

Original question: Find #lim_(x->oo)[-1/5(1-(1/x)^(4/5))]#

Note that #lim_(x->oo)1/x=0#

By substituting #x=oo# and using the above statement, we see that the original expression becomes: #lim_(x->oo)[-1/5(1-0^(4/5))]# #=lim_(x->oo)[-1/5(1)]# #=-1/5#

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Answer 2

Elijah Abram

To find the limit of the given expression as x approaches infinity, we can simplify it by applying the properties of limits.

First, let's simplify the expression inside the parentheses: (1 - (1/x))^(4/5).

As x approaches infinity, 1/x approaches 0. Therefore, we can rewrite the expression as (1 - 0)^(4/5), which simplifies to 1^(4/5) = 1.

Next, we multiply the simplified expression by -1/5: -1/5 * 1 = -1/5.

Therefore, the limit of the given expression as x approaches infinity is -1/5.

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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.