MathAnalysisCalculusLimits

The first and second wonderful limits

Apply the first wonderful limit or not

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Can the first wonderful limit be used to find the next limit?

$\lim\limits_{y\to0} \dfrac{\sin (8y^2 + 5y + 1)}{8y^2 + 5y + 1}$

Select one option from the list

No, because

8y^2 + 5y + 1

is not tend to

0

, if

y \to 0

Yes, because because we can replace

8y^2 + 5y + 1=z

and we will get the first wonderful limit.

No, because the first wonderful limit contains the

x

and in this example there is no variable

x

Yes, beacuse

8y^2 + 5y + 1

tends to

0

, if

y \to 0

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