How do you evaluate the limit #(2^x+sinx)/x^4# as x approaches #0#?

Answer 1

#oo#

Let's focus on the numerator first.

#lim_(xrarr0)(2^x + sin(x)) = 2^0 + sin(0) = 1#

Overall limit is:

#lim_(xrarr0)1/(x^4) = oo#
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Answer 2

To evaluate the limit (2^x+sinx)/x^4 as x approaches 0, we can use L'Hôpital's Rule. Taking the derivative of the numerator and denominator separately, we get (ln(2)*2^x+cosx)/4x^3. Substituting x=0 into this expression, we find the limit is ln(2)/0, which is undefined.

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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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