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Thread: Inequality Proof (fitzpatrick review 8, q5d)

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    Inequality Proof (fitzpatrick review 8, q5d)

    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
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    Re: Inequality Proof (fitzpatrick review 8, q5d)

    Quote Originally Posted by jaccs View Post
    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.
    “Smart people learn from their mistakes. But the real sharp ones learn from the mistakes of others.”
    ― Brandon Mull

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    Re: Inequality Proof (fitzpatrick review 8, q5d)

    Quote Originally Posted by jaccs View Post
    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.
    integral95 likes this.

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    Re: Inequality Proof (fitzpatrick review 8, q5d)

    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.

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