δ-ε proof of lim sin(x) = 0 x→0

[devout swift]

Am I doing this correct? Answer is not provided in the book and I wanna make sure

[zinc dagger]

hmmm

the sin inverse stuff is unnecessary and probably not part of the intended solution even if it will work

you’d need to use facts about sin inverse to make it work, while it’s simpler to just use the fact in the hint

[devout swift]

I understand, still unsure as to how to turn |sin(x)|≤|x-0| to the form of x<δ though

[zinc dagger]

basically just prove lim x -> 0 of x is 0

then you can slide the |sin(x)| in

i'll just write out what i mean: let $\varepsilon>0$, let $\delta = \varepsilon$. if $x$ satisfies $0<|x| < \delta$ then $|\sin(x)| < |x| < \varepsilon$

[lavish olive]

💜𝓁𝒶𝓎𝓁𝒶💜

[low verge]

my professor solved it for us in class

if you want i can send it if needed

ah nevermind he proved it for any a ntot for 0

[devout swift]

Thank you for the help! this is much clearer now.

.close

[fading canyon]

Solved

Post marked as solved by @devout swift.

Use .unsolved if this was a mistake.