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...
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...
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...
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...
[SOLVED] Maximum area/volume problems
I have two here. One I feel I've solved but am just looking for reassurance (I'm needy that way!), The other I've got an answer but I know I've missed something.
Homework Statement
1. A rectangle is inscribed in a 6/8/10 cm right-angle triangle where two...
Homework Statement
Suppose the graph f''(x) of a function is given by:
(see attachment)
(a) Find all points of inflection of f(x)
The Attempt at a Solution
First I figured, by looking at the graph and seeing the intercept points [(-2,0),(0,0),(2,0)] that f''(x) = x^{4}-4x^{2}
solving for...
Help please on these. I'm extremely rusty with differentiation and want to know if I've got the right answers here
Homework Statement
differentiate the following functions (you do not have to simplify):
a. f(x)=(x-2)^{3}e^{-2x}
b. f(x) = cos x / ln (x^{2} + x)
c. g(t) = cos^{4}(t^{2} +...
Is this all correct? (more bl**dy vectors!)
I hope these are right, but I have the nagging suspicion that they're not? Where have I gone wrong (if I have indeed gone wrong)?
Homework Statement
line P has equation (x+3)/2 = y = z-1
(a) Show that point Q (2,1,2) does not lie on line P.
(b)...
Homework Statement
following equations represent lines P nad Q in 3 dimensional space:
P: 2-x=y+1=(z-3)/2
Q: 5-x=y-2=(z+1)/2
(a) Show that P & Q are two different lines which are parallel
(b) Find the distance between the two lines, measured along a line perpendicular to P & Q.
Homework...