The question I'm stuck on is this:
Let f(x,y) = (x+1)^2 + y^2
I'm asked to find the partial derivatives and then evaluate them at (1,2). From there, find L(x,y), the linear approximation to f(x,y) at (1,2).
That part I'm ok with. I got the following:
f_x(x,y) = 2(x+1)
f_y(x,y) = 2y...
Thanks for the replies. It's helped me get my head around these problems better.
I like jbunniii's solution. very clever and succinct.
For this question:
\lim_{n \to \infty} \frac {n^p}{a^n} = 0
my solution is:
Apply L'Hopital's Rule:
\frac{p}{ln(a)} [\lim_{n \to \infty} \frac...
I've got a couple of problems I'm stuck on. Any help gratefully received!
Test for convergence/divergence:
\sum_{n=1}^{\infty} \frac {(n+1)}{n^3 ln(n+2)}
What test should I do here? Can I rearrange the equation to be:
\frac{(\frac{1}{n^2} + \frac{1}{n^3})}{ln(n+2)}
and then use...
I've got this question to do:
A bank is attempting to determine where its assets should be invested during the current
year. At present $500 million is available for investment in bonds, home loans, car loans,
and personal loans. The annual rate of return on each type of investment is known...
sorry I should have stated the problem a bit more in detail.
Once I've got the eigenvalues, I'm to put them into the equation
\lambda1x^2 + \lambda2y^2 = 9
so knowing which is which is important as swapping produces vastly different graphs with either:
9x^2 - y^2 = 9 giving x^2 - y^2/9 = 1...
I have a problem with determining eigenvalues. This is what I've got thus far:
Homework Statement
Identify and sketch the graph of the quadratic equation
4x² + 10xy + 4y² = 9
The Attempt at a Solution
We put it in the matrix form:
\begin{pmatrix} 4 & 5 \\
5 & 4 \\
\end{pmatrix}
Now we find...
Question One:
Train B travels 10km/hr faster than train A. Thus it's speed, relative to A, is 10km/hr.
Train A leaves 1/2 hour earlier meaning, at 25km/hr, it's 12.5km ahead.
So how long will it take train B, moving at a relative speed of 10km/hr, to travel 12.5km?
think about it a second:
you've already found that x^{2} - 8x + 11
Now you need to find y - 8y^{1/2} + 11
If you substituted x^{2} = y,
you would have x^{2} - 8x + 11
which you already have the answer to. If x = 4+/-\sqrt{5},
what is x^{2} (i.e. y) going to equal?
yay, got it right! Off to the post office I scurry.
And that other bit just came out poorly due to bad formating. It looks better in my assignment :wink:
Okay, I'm 99% sure I've got the right answer here, but I just wanted to make certain before I send my assignment in. It's the last question and has been bugging me for the last few days until I had an eureka moment just a few minutes back.
(In case you're wondering, I'm doing my studies by...
Sometimes it's easier to stick with whole numbers and fractions:
length of side = \sqrt{3}
length of QT = \frac{1}{2}\sqrt{3}
area of triangle QTS = \frac{1}{2}*\frac{\sqrt{3}}{2}*\sqrt{3}
=\frac{\sqrt{3}}{2}*\frac{\sqrt{3}}{2}
and what does \sqrt{3}*\sqrt{3} = ?
divide that by 4 (1/2 *...
Just a little. It wasn't helped by HoI using the wrong number! (it should read 10/3 not 4/3 - the 4/3 is correct but HoI skipped a line). Also you're only / by H in your equation whereas you should be / by W + H.
Here's how I'd do it:
Let's call the time taken to drive home x.
Time taken...
Okay. Here's what I got for the box question:
base of box = x, height = h.
Volume of box = x²h = 2000; therefore h = 2000/x²
Surface area of box = 2x² + 4xh
Assume the sides cost $a p/cm².
Then the total cost of the sides will be 4axh. Since the top and bottom cost twice as much (ie...