K9-47G

That's interesting.

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.

Has anyone here read it? What did you think of it?

I got 4.3

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.

I noticed that if I type .9999999999 (ten nines) into my TI-83 calculator and press enter, it gives me the answer to be .9999999999 (ten nines), But if I type .99999999999 (eleven nines) into my calculator and press enter it gives the answer to be one. I suppose my TI-83 rounds to the 10th decimal place.

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]

Ok, thanks a lot.

Can you tell if those answers are right?

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]

I think the second one has to do with the purple squares in the background.

This problem reminds me of the many examples that Richard Dawkins gave in his book, The Selfish Gene.

11131221133112132113212221 whew.

Can you please check if my answer is correct.

[math] y=sin(sin(sinx)) [/math]

[math] y'=cos(sin(sinx))cos(sinx)cosx [/math]

(My calculus professor doesn't want our answers simplified.)

ok, thanks.

[math] g^{(n)}(x)=-n(-1^n)e^{-x}+(-1^n)xe^{-x} [/math]

How do you format your math work to look bold and easier to read?

So would my formula be g^n(x)= -n(-1^n)e^-x+(-1^n)xe^-x. I know there must be an easier way to write that.

The inductive proof is: show true for n=1, assume true for n=k and show true for n=k+1, right?

so e^-x derived is -e^-x.... We haven't covered that yet.

Now I'm getting

g'(x)=e^-x-xe^-x

g''(x)=-2e^-x+xe^-x

g'''(x)= 3e^-x-xe^-x

and so on, but I have no idea how to make an explicit formula out of that because the negatives are alternating.

well I did write it out, this is what I got.

g'(x)= xe^-x+e^-x

g"(x)= xe^-x+2e^-x

g'''(x)= xe^-x+3e^-x

so I concluded that the formula would be g^n(x)= g(x)+n(e^-x). I'm just not sure if my math is right.

So would it be g^n(x)=g(x)+n(e^-x)..... I'm assuming that the derivative of e^-x is e^-x....

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).

Thank you so much!

Can someone tell me the limit of (x/(2x-2))-(1/((x^2)-1)) as x approaches 1.