Year 12s: what will be the first way you research your future options? >>

draw ln( 1 + 1/x ) :S

cheena

hey

how wolud you go about drawing ln( 1 + 1/x)

thanks :wink:

Reply 1

nuodai

Write it as

\ln \dfrac{x+1}{x}

and use the laws of logs to break it down a little, then you can look for stationary points and what happens as

|x| \to \infty

Spoiler

Reply 2

electriic_ink

Well there's gonna be vertical asymptotes at x=0 and when x=-1. Will there be any horizontal asymptotes? Consider what happens when -1 < x < 0 and when x < -1 and when x > 0.

You don't really need to rewrite it in order to draw it but like nuodai said, look at the gradient.

Reply 3

cheena

thanks
i got it

the question i had was to prove

(ln (x) )/x > ln(1 + 1/x)

for x>2

i tried to draw the graphs and compare since i couldnt quite get it with induction
could you guys give me a hint of how i should do it
thanks again :wink:

Reply 4

electriic_ink

The only way I could think of would be to draw each graph (it's not that hard) and then algebraically find their intersection point.