Inequality Proof (fitzpatrick review 8, q5d) (1 Viewer)

[jaccs]

Trying to prove part d of the inequality proof from fitz chapter 8 review, question 5

parts a-c are fine

part d am stuck

from previous parts got as far as



and I₁=2ln2-1

but can't finish the proof

did try replacing (ln 2)² with just ln 2 as (ln 2)² > ln2

any help greatly appreciated

 

[integral95]

Trying to prove part d of the inequality proof from fitz chapter 8 review, question 5

parts a-c are fine

part d am stuck

from previous parts got as far as



and I₁=2ln2-1

but can't finish the proof

did try replacing (ln 2)² with just ln 2 as (ln 2)² > ln2

any help greatly appreciated

That's not even true since you're squaring a number less than 1






At the moment I still can't figure the lower bound either.

 

[InteGrand]

Trying to prove part d of the inequality proof from fitz chapter 8 review, question 5

parts a-c are fine

part d am stuck

from previous parts got as far as



and I₁=2ln2-1

but can't finish the proof

did try replacing (ln 2)² with just ln 2 as (ln 2)² > ln2

any help greatly appreciated

HINT: Using what you have, obtain a quadratic inequality for ln 2 and solve the inequality. This will get you (both of) the desired bounds.

 

[jaccs]

Thank you Integrand, that worked beautifully. You are genius.

Thanks integral95, that squaring was really careless of me, didn't even occur to me that it was less than 1, hence that inequality wouldn't hold, was just so desperate to get rid of the square... argghhh. will watch out for that in future.

thank you both, really appreciate it.