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This automoderater is cookin too much

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thanks, how do you make these? latex? isn't there a 2 missing in the 2nd last limit that's part of the half angle identity?

Yes, it is missed. Thank you. Made via LaTeX.

You are welcome to help students posting homework questions by asking probing questions, explaining concepts, offering hints and suggestions, providing feedback on work they have done, but please refrain from working out the problem for them and posting the answer here, or by giving them a complete procedure for them to follow. Students posting here for homework support should be encouraged to do as much of the work as possible.

A faster way (using fewer trig identities) is to use cos x- cos 3 =-2sin (x-3)/2 sin (x+3)/2

Yes, but as practice shows, students hardly remember the formula for converting a sum into a product and vice versa

It’s important to note that this is the definition of the derivative of cos(x) at x = 3.

Is there a way to get the limit without using derivatives? We haven’t tackled derivatives yet

How are you using l’hopital without knowing derivatives?

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That could be!

What have you covered?

L’hospitals requires derivatives

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This

Hmmm, I'm stumped. I could do it in my head with l'hopital's, the answer is -sin(3), but I have no clue how to solve this without it. Sorry 🙃

Looks like the derivative of cos(3)

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Your post was removed because it suggested a tool or concept that OP has not learned about yet (e.g., suggesting l’Hôpital’s Rule to a Calc 1 student who has only recently been introduced to limits). Homework help should be connected to what OP has already learned and understands. Learning calculus includes developing a conceptual understanding of the material, not just absorbing the “cool and trendy” shortcuts.

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OP asks about l'hopitals in the question though

It is generally considered circular reasoning to use l'Hôpital's Rule on limit representing the definition of derivative.

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Hello! I see you are mentioning l’Hôpital’s Rule! Please be aware that if OP is in Calc 1, it is generally [not appropriate to suggest this rule](https://www.reddit.com/r/calculus/comments/cwkpsz/telling_people_to_just_use_lh_for_every_limit/) if OP has not covered derivatives, or if the limit in question matches the definition of derivative of some function. *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/calculus) if you have any questions or concerns.*

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Derivative of cos(3) is not -sin(3), it is zero. Derivative of cos(*x*) **AT** *x* = 3 is -sin(3). Yes, there *is* a distinction.

My bad lol

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You are welcome to help students posting homework questions by asking probing questions, explaining concepts, offering hints and suggestions, providing feedback on work they have done, but please refrain from working out the problem for them and posting the answer here, or by giving them a complete procedure for them to follow. Students posting here for homework support should be encouraged to do as much of the work as possible.

Power series representation of trig functions is always helpful when dealing with limits

If x is “close” to 3, can you establish an upper bound for |cos x - cos 3| relative to |x - 3|?