Indetermination or 1 | limits

Here we have the initial operation

And here the problem arises: can you clear the sine knowing that it is worth zero? Is there a rule that allows it?

If not, the result is undetermined

#Calculus

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
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Comments

When we are dealing with limits, we are allowed to cancel out terms which would technically make the answer undefined. This is because the limit of a function is different than the actual value of the function at that limit. The limit is asking "What does this function approach?", not "What does this function equal?". Thus, your first method is correct. Try graphing it on a graphing calculator like Desmos and you'll see that while the function looks like it equals $1$ at $\theta = 0$ , it is really undefined. Hope this helps.

David Stiff - 6 months, 1 week ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$