# K9-47G

Senior Members

39

## Posts posted by K9-47G

### The vegetative state and awareness

That's interesting.

### Matt Ridley's "Genome"

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.

### Matt Ridley's "Genome"

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

I got 4.3

### Optimization

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 $dr/dt$ to be the speed on the road which is 4 mph, and $do/dt$ 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.

### Ending the 0.999~ = 1 debates

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.

### Derivatives: Some Questions...

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..

$y= (\ln x)^{\sin x}$ is the same as $\sin x\ln x$

### Derivatives: Some Questions...

Ok, thanks a lot.

### Derivatives: Some Questions...

Can you tell if those answers are right?

### Derivatives: Some Questions...

1) Find $\frac{d}{dx} log(lnx)$

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

$\frac{1}{x(lnxln10)}$

2) Find the slope of the line tangent to the graph $cos(xy)=y$ at $(0,1)$

$-sin(xy)(y)+(xy')=y'$

$-ysin(xy)=y'-(xy')$

$\frac{-ysin(xy)}{1-x}=y'$

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

3) If $y=(lnx)^{sinx} x>1,$ Find $y'$

$sinxlnx=sinx\frac{1}{x}+(cosx)(lnx)$

$\frac{sinx}{x} +cosxlnx$

$1+cosxlnx$

### Harder than what they Look?

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

### Hard Question!

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

### 1?

11131221133112132113212221 whew.

### derivative of sin(sin(sinx))

$y=sin(sin(sinx))$

$y'=cos(sin(sinx))cos(sinx)cosx$

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

ok, thanks.

### derivative of g^n(x)

$g^{(n)}(x)=-n(-1^n)e^{-x}+(-1^n)xe^{-x}$

### derivative of g^n(x)

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

### derivative of g^n(x)

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.

### derivative of g^n(x)

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

### derivative of g^n(x)

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.

### derivative of g^n(x)

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.

### derivative of g^n(x)

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

### derivative of g^n(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).

### Can someone tell me the limit of...

Thank you so much!

### Can someone tell me the limit of...

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

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