Question

A Qu

Answer 1

Mini-Challenge for Voca:

\(\left. \dfrac{x + \sin x}{x} \right|_{x \to 0}\)

Answer 2

re-write as \[\frac{ x }{ x }+\frac{ \sin(x) }{ x }\]

it's not the best proof but I remember we used the squeeze theorem to prove that sin(x)/x approaches 1 as x -> 0 making the entire limit 2

would like to see how you would approach this ;;

Answer 3

That's the perfect answer I**M**HO, especially the ref to the Squeeze Theorem result.

You can quote these as given:



I'm not sure there's any other way to do it.

Try this one too, if you like:

\(\left. \dfrac{x + \sin x}{x} \right|_{x \to \color{red}{\infty}}\)

This is another, more obvious, L'Hôpital's Rule trap, which is what I am kinda trying to understand better for myself. But the way you're doing it means you don't have to care about L'H.

Answer 4

sin(x)/x has a limit of 0 as x -> infinity by virtue of the numerator being limited to +/- 1 and the denominator going to infinity

so the second limit ends up being 1

Answer 5

TU Voca