For the first question, is it as

?

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For the second question, let

be a sequence that converges to

and

. (We want to show that

.) Because of convergence,

such that

, and

such that

.

So if

, by the triangle inequality,

. Since

was arbitrary, we can conclude that

.

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For the third question, you know this function is continuous at

(because it is a composition of continuous functions), so you can just plug in

for

to get

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For the fourth question,

and

, so by the Intermediate Value Theorem

such that

.

Similarly,

so the IMT says that

such that

.

Similarly,

so the IMT says that

such that

.

Thus there are 3 zeroes in

.

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I hope I was some help.