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Math Help - Transcendental equations: derivatives, integrals, limits,

  1. #1
    Junior Member plm2e's Avatar
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    Transcendental equations: derivatives, integrals, limits,

    I have to help teach this class tomorrow for my Senior Seminar Math class. The lesson is over Exponential and Logarithmic Functions and L'Hospital's Rule. I have all the problems needed to review this lesson, but i can not solve any of them. My teaching partner and I have had schedule conflicts and we are now on our own. It is late starting but any help or advise would be greatly appreciated. I have not had calculus in 5 years.

    1. y=√(2)*e^(√(2)x) y` =?
    2. y=ln(sec^(2)x) y`=?
    3. y=9^(2t) y`=?
    4. y=[2(x^2+1)]/[√(cos 2x)] y`=?

    EVALUATE INTEGRALS
    5. ∫ e^t * cos(3e^t - 2) dt
    6. ∫(top: π/6, bottom: -π/2) (cos t)/(1-sin t) dt
    7. ∫ [ln(x-5)]/(x-5) dx
    8. ∫(top: e, bottom: 1) (1/x) * (1+ 7 ln x)^(-1/3) dx
    9. ∫(top:3, bottom: √3) dt/(3+t^2)

    Solve for Y
    10. 3^y = 3 ln x y=?

    11. lim (x→0) (3^x - 1) / x
    12. lim (x→0) (4 - 4e^x) / xe^x
    13. lim (y→0+) e^(-1/y) ln y

    My partner has the other 13 problems and his are basically the same. I know this is a lot but any help with any of these would be greatly appreciated.
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  2. #2
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    mr fantastic's Avatar
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    Quote Originally Posted by plm2e View Post
    I have to help teach this class tomorrow for my Senior Seminar Math class. The lesson is over Exponential and Logarithmic Functions and L'Hospital's Rule. I have all the problems needed to review this lesson, but i can not solve any of them. My teaching partner and I have had schedule conflicts and we are now on our own. It is late starting but any help or advise would be greatly appreciated. I have not had calculus in 5 years.

    1. y=√(2)*e^(√(2)x) y` =?
    2. y=ln(sec^(2)x) y`=?
    3. y=9^(2t) y`=?
    4. y=[2(x^2+1)]/[√(cos 2x)] y`=?

    EVALUATE INTEGRALS
    5. ∫ e^t * cos(3e^t - 2) dt
    6. ∫(top: π/6, bottom: -π/2) (cos t)/(1-sin t) dt
    7. ∫ [ln(x-5)]/(x-5) dx
    8. ∫(top: e, bottom: 1) (1/x) * (1+ 7 ln x)^(-1/3) dx
    9. ∫(top:3, bottom: √3) dt/(3+t^2)

    Solve for Y
    10. 3^y = 3 ln x y=?

    11. lim (x→0) (3^x - 1) / x
    12. lim (x→0) (4 - 4e^x) / xe^x
    13. lim (y→0+) e^(-1/y) ln y

    My partner has the other 13 problems and his are basically the same. I know this is a lot but any help with any of these would be greatly appreciated.
    If you're teaching this stuff you must have some idea how to do it? Where are you stuck? What have you tried?

    "My teaching partner and I have had schedule conflicts and we are now on our own." What does this mean ...... someone else was originally going to give you the solutions and you were just going to copy them onto the board for the class to write down?
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  3. #3
    Junior Member plm2e's Avatar
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    Quote Originally Posted by mr fantastic View Post
    If you're teaching this stuff you must have some idea how to do it? Where are you stuck? What have you tried?

    "My teaching partner and I have had schedule conflicts and we are now on our own." What does this mean ...... someone else was originally going to give you the solutions and you were just going to copy them onto the board for the class to write down?

    No, we have to get up in front of class and go over these problems. I have been waiting on my partner to help me because he said he knew the subject. everytime we were supposed to meet up, something happened. We are now on are own because it is too late to get help from my instructor. I said i would attempt to get help with these 13 problems.

    I understand derivatives and intergration. I have all the rules down, but when it comes to logarithmic or exponential, I am seriously lost. The limit -problems I can get on my graphing calculater, but i need to know how to work them.
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  4. #4
    Super Member Showcase_22's Avatar
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    Well i'm an A-level student off to university this week and i've exhausted all my material. Thanks for posting these!

    However, I agree with Mr Fantastic that I would like to see the methods you've tried. It just makes it more interesting to try and find out why that method doesn't work, or if there's another method worth trying.

    This is what I did:

    Integrals:











    Question 10 is just a simple log problem (looks like it). I'm not that good with limits since I haven't learnt about them yet so i'll go on and do the differentials (i've left the last one for you, it's the quotient rule and it's not that challenging once you know how!).

    Differentials:

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  5. #5
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    Advice? I wouldn't do it, not tomorrow at least and I wouldn't rely on my partner: have a backup. I'd postpone the lecture until next week, learn how to do each and every problem, go into great detail why the solution works, elaborate (change) the problems and show how the changes affect the solutions, and oh yea, plots, overheads, and throw in some Mathematica programming for Lagniappe and finally, go out of my way to never, never, get into this situation ever again. For heavens sake, it's for a grade I presume and you're setting yourself up for failure not to mention possibly tramuatizing the students with ineffective teaching skills.

    There, I said it. It's tough I know. Just offering my advice.
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by plm2e View Post
    I have to help teach this class tomorrow for my Senior Seminar Math class. The lesson is over Exponential and Logarithmic Functions and L'Hospital's Rule. I have all the problems needed to review this lesson, but i can not solve any of them. My teaching partner and I have had schedule conflicts and we are now on our own. It is late starting but any help or advise would be greatly appreciated. I have not had calculus in 5 years.

    My partner has the other 13 problems and his are basically the same. I know this is a lot but any help with any of these would be greatly appreciated.
    I don't suppose you have the time to answer this, but I'm curious so will ask any way.

    What course are you studying that you have to give this lesson, seminar or demonstration for? And what are the audience studying and at what level?

    RonL
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  7. #7
    Junior Member plm2e's Avatar
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    Quote Originally Posted by CaptainBlack View Post
    I don't suppose you have the time to answer this, but I'm curious so will ask any way.

    What course are you studying that you have to give this lesson, seminar or demonstration for? And what are the audience studying and at what level?

    RonL

    i have an extension till thursday.

    I am an actuarial science major who has been out of school for 4.5 years. The class is my MATH 4990 class, which is seminar in mathematics. It is a required class for all seniors graduating with math majors. I am teaching this to my 4990 class
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