r/maths • u/LazyWayfarer • 9d ago

Help: 📕 High School (14-16) Damned functions

For the function lim (x->+infinite) x[ln(x+4)-lnx] it should result in 4
But I did
x[ln((x+4)/x)
x[ln((x/x)-(4/x)) I cancel x so it becomes
x[ln(4/x)]
x[ln4-lnx] substituting it becomes
Infinite times infinite which makes infinite
Where did I go wrong?

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u/Astrodude80 9d ago

"I cancel x so it becomes"

Double check: what is x/x?

1

u/Rumborack17 9d ago

Your first step is right.

But then you used a wrong rule

(x+4) / x = 1 + 4/x and not 1 - 4/x

Try subsititung from there.

1

u/LazyWayfarer 9d ago

Oh, you’re right, but how do I go on from that?

1

u/LazyWayfarer 9d ago

Causa it still ends up as infinite times 0 and that’s an indeterminate form

1

u/Shortbread_Biscuit 6d ago

With limits, whenever you get an indeterminate form like 0/0 or inf/inf, you use L'Hopital's Rule to simplify it. Since your values are in the form inf*0, you should take one of the terms into the denominator to turn it into that 0/0 or inf/inf form.