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How do you find the limit of #rootx(x)# as #x>oo#?

Answer 1

Scarlett Allison

#lim_(x->oo) root(x)x =1#

We can write #f(x) = root(x)x# as:

#f(x) = root(x)x = (x^(1/2))^(1/x)=x^(1/(2x))=e^(lnx/(2x))#

so, as:

#lim_(x->oo) lnx/(2x)=0#

#lim_(x->oo) root(x)x = lim_(x->oo)e^(lnx/(2x))= e^0=1#

graph{root(x)x [-0.75, 19.25, -4.88, 5.12]}

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Answer 2

Emma Aldridge

To find the limit of √(x) as x approaches infinity (∞), we can use the concept of limits.

As x becomes larger and larger, the value of √(x) also increases. However, it does not grow indefinitely.

To determine the limit, we can consider the behavior of the function as x approaches infinity. In this case, the function √(x) approaches infinity as well.

Therefore, the limit of √(x) as x approaches infinity (∞) is also 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 of #rootx(x)# as #x&gt;oo#?

How do you find the limit of #rootx(x)# as #x>oo#?