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Problem 41 Easy Difficulty

Each limit represents the derivative of some function $ f $ at some number $ a $. State such an $ f $ and $ a $ in each case.

$ \displaystyle \lim_{h \to 0} \frac{\cos (\pi + h) + 1}{h} $

Answer

$f(x)=\cos (x) ; a=\pi$

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Video Transcript

we have a question and this uh we need to find the value of function efforts and ah quantity is there? It is. What we say it is derivative. Okay, so we have a formula for basic formula for derivative F dash a equal to Limit accidents to zero F April such limit That's tends to zero F A place at minus mm hmm. If they buy it F A by at and we have given quantity limit at not going to the expression course X. Let's get sorry caused by plus set bible assets minus F A. It is one here divide by at. So everything seems to be, everything seems to be normal at for it and as for it so they will be able to pie which means we can see that have facts equal to of course X. Okay. So uh if you write F A plus it it will be by plus set and equal to pi So that F of pie or I hope they will be caused by which is equal to Cameed by is equal to -1. of course by is -1. So Okay, okay, which is minus one. Sorry, it is plus one. Yes, of course it is great because this could be written as limit its approaches to zero of course five plus at minus minus one by at after comparing we can get affects equal to cossacks and equal to pi. Thank you so much