Homework Statement
Given a matrix A. So I can reduce A to ref(A). Let's say in ref(A), the columns that contain leading ones are column 1, 3, and 5. True or false:
(a) Columns 1, 3, and 5 from ref(A) form the column space of ref(A).
(b) The corresponding column 1, 3, and 5 from the original...
Homework Statement
I have this statement:
If M(x,y)dx+N(x,y)dy=0 is a homogeneous DE, then μ(x,y)=\frac{1}{xM+yN} is its integrating factor. The problem is, how do we derive this integrating factor?
Homework Equations
For homogeneous DE, we have f(kx,ky)=k^n*f(x,y)
We also have...
Since the question says d is an integer, I try to use other types of 'combination', and when I tried with '6, 9, 7, d' going clockwise, I get d = 2. Yay! Thanks again, eumyang, for the help :)
Homework Statement
This question is taken from 2011 Malaysian Mathematical Olympiad.
Mary is standing in a rectangular garden. Her distance to the four corners of the garden are 6 m, 7 m, 9 m and d m, respectively, where d is an integer. Find d.
Homework Equations
Triangle...
Can I use the series expansion?
\frac{sin^{-1}x}{x}
=\frac{x+\frac{X^3}{6}+\frac{3x^5}{40}+...}{x}
=1+\frac{x^2}{6}+\frac{3x^4}{40}+...
Then I can get limit = 1 when I substitute x = 0.
Can we get the same answer without using the series expansion thingy?
Another question:
Find the limit of \frac{sin^{-1}x}{x} when x approaches 0.
The answer given is 1.
Seems like I can't express arcsin explicitly. Any clue on how to start? :)
Yay, I get it. I multiply by another conjugate and eventually the (2-x) term will cancel out. Then I will get 2/4 which is equal to 1/2. Thanks so much for the help. :)
\frac{\sqrt{6-x}-2}{\sqrt{3-x}-1}
=\frac{(\sqrt{6-x}-2)(\sqrt{3-x}+1)}{(\sqrt{3-x}-1))(\sqrt{3-x}+1)}...
Oops, sorry. Now I have
\frac{\sqrt{6-x}-2}{\sqrt{3-x}-1}
=\frac{(\sqrt{6-x}-2)(\sqrt{3-x}+1)}{(\sqrt{3-x}-1))(\sqrt{3-x}+1)}
=\frac{(\sqrt{6-x}-2)(\sqrt{3-x}+1)}{2-x}
Homework Statement
Find the lim of \frac{\sqrt{6-x}-2}{\sqrt{3-x}-1}when x approaches 2, without using L'hopital rule or the definition.
Homework Equations
The Attempt at a Solution
I try to multiply both the numerator and the denominator to get \frac{(\sqrt{6-x}-2)(\sqrt{3-x}-1)}{2-x}, but...
Homework Statement
Given that the values for a, b, c, d, e and f for the system ax+by=e, cx+dy=f has two different solutions. Show that ax+by=0, cx+dy=0 also has two different solutions.
Homework Equations
The Attempt at a Solution
There're three cases of how two straight lines...
Homework Statement
P = [data(1:65,11:100) data(1:65,411:500)]; % Input, all together 180 data set, 65 dimension
T = [ones(1,90) zeros(1,90);
zeros(1,90) ones(1,90)]; % Actual output, first 90 data set belong to class I and the next 90 belong to class II
net =...
Homework Statement
Is there any difference between the two notations below? Or can they be used interchangeably?
\tilde{x} and \underline{x} (not an underline, but the tilde is at the bottom of the unknown x)Homework Equations
The Attempt at a Solution
From my observation, \underline{x} is...