Jump to content


Senior Members
  • Posts

  • Joined

  • Last visited

Posts posted by K9-47G

  1. No, it's not a novel. He talks a lot about findings from the Human Genome Project. I suppose as far as books are concerned it's comparable to much of Dawkin's works. Informational, but with a more laid-back approach.

  2. This is one optimization problem that I just cant figure out. I'll post what I have...



    A hiker at point A on a straight road wants to reach, in the shortest time, a point B located 6 miles from the road and 10 miles from point A. The hiker's speed on the paved road is 4 mph and only 2 mph off the road. How far should he continue on the road before heading in a straight line for the point B?


    I am pretty sure I would have to use the pythagorean theorem because if you draw the problem you get a triange with two sides given. Plus I denoted [math] dr/dt [/math] to be the speed on the road which is 4 mph, and [math] do/dt [/math] to be the speed off road which is 2 mph. I just don't know how to find my objective function. Any help would be appreciated.

  3. For number 3, I thought I would use the logarithmic power rule (not sure of the real name) and therefore the exponent, sinx, can be written as the first term in problem. Then I used the product rule to find the derivative..


    [math] y= (\ln x)^{\sin x} [/math] is the same as [math] \sin x\ln x [/math]

  4. 1) Find [math] \frac{d}{dx} log(lnx) [/math]

    I assume that the log has a base of 10, so I got


    [math] \frac{1}{x(lnxln10)} [/math]


    2) Find the slope of the line tangent to the graph [math] cos(xy)=y [/math] at [math] (0,1) [/math]


    [math] -sin(xy)(y)+(xy')=y' [/math]


    [math] -ysin(xy)=y'-(xy') [/math]


    [math] \frac{-ysin(xy)}{1-x}=y' [/math]


    Then I just keep getting 0 when I substitute (0,1) in...


    3) If [math] y=(lnx)^{sinx} x>1, [/math] Find [math] y' [/math]


    [math] sinxlnx=sinx\frac{1}{x}+(cosx)(lnx) [/math]


    [math] \frac{sinx}{x} +cosxlnx [/math]


    [math] 1+cosxlnx [/math]

  5. This is the problem in my book. If g(x)=x/e^x, find g^(n)(x). I don't really understand what the problem is asking me to find. It is in the differentiation section of the book, if that helps at all. I think it may be asking for a formula... By the way, the n in the formula represents how many times to take the derivative of g(x).

  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.