s

So, I was given an assignment to use a computer algebraic system to compute a double integral. I also needed to result to be correct to the 4th decimal place.

I decided to use Wolfram Alpha, and they gave me an answer of :

∫ ∫ sqrt(100(x^4)(cos^2(y))+64(x^4)(sin^2(y))+390x^2) dy dx = 294.592

for x [0,2] and y[0,2pi]

How do I get another decimal? I got the 7 day free trial for Wolfram Pro, and tried the "extended computation time," but after clicking it all it does is glow red for x amount of minutes.

Is anyone familiar with Wolfram that can help me?

Thanks.

Hi,

I have a question regarding Orthogonal sets and projections.

Say we have the vectors y = [3, -1, 1, 13], v(1) = [1, -2, -1, 2] and v(2) = [-4, 1, 0, 3]

The projection of y, or y hat, would be found using the equation:

y hat = (y • v(1))/(v(1) • v(1)) * (v(1)) + (y • v(2))/(v(2) • v(2)) * (v(2))

IF the set is orthogonal.

But what do we do if it isn't orthogonal? How would we find the projection of y then?

I read through my textbook today but cannot seem to find what I'm looking for...

Any help would be greatly appreciated!

Having a hard time on this:

During light activity, a 71 kg person may generate 214 kcal/h. Assuming that 21% of this goes into useful work and the other 79% is converted to heat, estimate the temperature rise of the body after 1.00 h if none of this heat is transferred to the environment.

I did the following:

214 kcal/h * .79 = 169.06 / 71 = 2.38 (which is wrong)

Hi, I am having trouble answering the second part of this problem:

a) Calculate the rms speed of a nitrogen molecule at 0°C

I did the calculations and found Vrms= 492 m/s

b) Determine how many times per second it would move back and forth across a 7.9 m long room on the average, assuming it made very few collisions with other molecules.

This is where I am stuck. I tried to use the concept that in 1 second, it moved 492 m. And it moving back and forth meant 2*7.9m = 15.8m. The solution manual gives an answer of 18 /s. Can someone please explain? Thanks!

Can anybody tell me what this is? My 6 year old, spayed Shepherd-mix has begun to frequently scratch two areas in her underbelly lately. In the picture below is the cause for her itching. There are two of them, symmetrical with one of the left and one on the right. Although she doesn't seem to be in pain, she scratches either "pimple" (?) quite often.

Her diet has remained the same for the last 3-4 months and she is up-to-date with all medications (for fleas, etc). I'm concerned for my dog but it does not seem serious enough to contact a vet... Can anyone identify this?

Picture: http://i.imgur.com/tmlNwTu.jpg?1

Thank you!

Can anybody tell me what this is? She isn't too bothered by it, but she has begun to scratch it noticeably more than her occasional itches.. Should I be concerned?

Picture: http://i.imgur.com/tmlNwTu.jpg?1

Thank you!

Estimate ∫cos(x^2)dx

hint: Use the error formula for alternating series

Here is my work thus far:

cosx = (d/dx)sinx = (d/dx)(Σ(n=0 to infinity) (-1)^n (x^(2n+1))/(2n+1)! =...= Σ(n=0 to inf) ((-1)^n (x^2n)/(2n)!

let x=x^2,

cosx^2 = x^2 - (x^4)/2 + (x^8)/4! -... = Σ((-1)^n (x^(4n))/(2n)!

Next, I integrate both sides

∫cost^2 from 0 to x = (x^3)/3 - (x^5)/5*2 + (x^9)/(9*4!) - ... = Σ((-1)^n (x^(4n+4))/(2n+2)!

so ∫cos(x^2) from 0 to 1/2 = .......

Taking the absolute limit when n approaches infinity, I get 0.

Now, I let lS-S(n)l< a(n+1)

And I plug n=1 into the series, getting 0.0001<0.0005

Finally,

S=S(1) where I only use the first term

S = (0.5^3)/3 = 0.000042

Is this method correct?

radius of convergence for:

f(x) = xln(1+2x)

My professor said to start with a power series that we are familiar with, namely:

Σx^n = 1/(1-x)= 1 + x + x^2 + x^3 .... for lxl<1

But I don't really know how to begin this problem

If I take the derivative of y= ln(1+2x), I get y' = 2/(1+2x)

But, I can't connect this with the known power series

Any help would be appreciated

Hey guys, need some help with this:

"Determine whether the sequence converges or diverges. If it converges, find the limit"

a(n) = (5e^n + 6e^-n) / (e^2n - 6)

I am more interested in how you solve this than getting an answer, so I would appreciate it if someone took the time to explain :)

Thanks!

My professor briefly went over alternating series this past week, but I am still unsure of what exactly it is that I need to do..

Here is what I am stuck on:

" Apply and error formula to estimate the series correct to four decimal places, that is, abs (R) < 0.00005, where R is the error or the remainder of the nth partial sum."

Σ [(-1)^n]/[(5^n)(n!)] from 1 to infinity

What I have start: Σ (abs ([(-1)^n]/[(5^n)(n!)]) = Σ (1/(5^n)(n!))

Do I take the integral from n to infinity next?...

Here's what I did for a simpler problem:

Σ (9/(n^8)), find the sum with an error less than 0.0001

error < 0.0001

S-S(n) < 0.0001

Σ [9/(k^8)] from n to infinity

S - S(n) < ∫(9/(k^8))dk = 9/(4n^4)

9/(4n^4) < 0.0001

9/4 < 0.0001n^4

22500 < n^4

12.15<n

Let n=13,

Σ (9/n^8) = 9/1 + 9/(2^8) +......

Is this how you solve the problem?

Having some trouble understanding the concepts of parametrics equations..

I am able to do:

x = 2cos(t), y = 4sin(t)

where: x^2/4 + y^2/16 = 1 is an ellipse

BUT,

I have no idea how to eliminate the parameters from the following:

1) x = 4cos(2t), y = 4sin(4t)

2) x = (8cos(t))/t , y = (8sin)t))/t

Any help is greatly appreciated!!

My homework assignment asks me to match each given graph with its corresponding parametric equations.

I'm blanking out...

Given: x = [8cos(t)]/t, y = [8sin(t)]/t

What are the steps to matching the graphs?

Thanks!

I have been looking for a clear explanation/method on finding how to determine if a given (improper) integral is convergent or divergent.

Using the following example, please explain step by step the most common method:

∫ (1 / (x^2 + x) from 1 to Infinity

Here's how my professor explained the textbook method:

Integrate from 1 to x,

∫ 1/(t^2 + t) dx

Where 1/(t^2 + t) = a/(t) + b/(t+1)

= ∫ (1/t) - (1/t+1) dt

= [lnt - ln(t+1)] from 1 to x

= lnx - ln(x+1) + ln2

And as the lim (lnx - ln(x+1) + ln2) as x approaches infinity,

Using L'hospitals rule,

lim (ln (x/ x+1)) = lim (ln (1/1) = 0

and we get 0 + ln2 = ln2

So I guess my only remaining question is... Is the determining factor for whether an integral is convergent or divergent relied solely upon whether (what we did above) is a finite or infinite number?

I have been looking for a clear explanation/method on finding how to determine if a given (improper) integral is convergent or divergent.

Using the following example, please explain step by step the most common method:

∫ (1 / (x^2 + x) from 1 to Infinity

Here's how my professor explained the textbook method:

Integrate from 1 to x,

∫ 1/(t^2 + t) dx

Where 1/(t^2 + t) = a/(t) + b/(t+1)

= ∫ (1/t) - (1/t+1) dt

= [lnt - ln(t+1)] from 1 to x

= lnx - ln(x+1) + ln2

And as the lim (lnx - ln(x+1) + ln2) as x approaches infinity,

ln(infinity) - ln(infinity) = infinity - infinity

IF my above steps are correct, what do I do next? If I am doing this problem incorrectly, I would appreciate it if anyone can take the time to point me in the right direction.

Links to any helpful websites are also greatly appreciated!

The problem is originally

Int( 1/(1+cos^2(x))

I divided top and bot by cos^2(x) and then let u= tanx, du= sec^2(x)

= int( 1/(2+u^2)

What can I do now?

Can someone clarify how I know whether a function is considered Top/Bottom during integration with respect to the X or Y axis?

Say I have y=x and y=x^2 bounded by x=2. Which is the "top" function?

My 4 year old German Shepard mix has barely sniffed her breakfast for the last two days.

She didn't eat her breakfast (only the scarce wet food that I mix with her kibbles) until my brother came home at 2PM today...

And while she did eat dinner, she only ate half of an already reduced meal...

My brother and I recently started taking summer classes after a 3 week break. Could my dog be protesting? (lol)

I take her out for walks everyday and she seems fine. She poops regularly and isn't acting out of norm other than her recent refusal to eat her meals.. We changed her kibbles and wet food about 2 weeks ago and she was fine with it. Treats are still eaten with a ferocity, so what's the problem?

Just started my summer semester Calculus class and feel a bit rusty...

For the following problem, I am confusing myself because I am unsure of what I can/cannot do:

A = ∫ [(√(x+2)) - (1/(x+1))]dx

Can I just split the two such that:

∫(√(x+2))dx - ∫(1/(x+1))dx

And then use U substitution separately?

Or do I combine the two such that:

∫[(x+1)√(x+2) - 1]/(x+1)dx

Again, I've become a bit rusty over my 3 weeks of freedom. I don't need you to solve the problem, just give me a nudge in the right direction.

Thanks!