Homework Statement
Determine convergence or divergence using any method covered so far*:
Ʃ(1/(n*ln(n)^2 - n)) from n = 1 to infinity
*The methods are the following:
- Dichotomy for positive series (if the partial sums are bounded above and the series is positive, the series converges)
-...
Homework Statement
Compute the area as an integral along the y-axis:
f(x) = x^2 - 6, g(x) = 6 - x^3
Homework Equations
N/A
The Attempt at a Solution
I solve for x in terms of y for both equations and end up with:
f(y) = +/-√(y+6), g(y) = (6-y)^(1/3)
I then look for interception points...
Homework Statement
dy/dt = k*y*ln(y/M), where M and k are constants.
Show that y = Meaekt satisfies the above equation for any constant a.
Homework Equations
y' = ky
y = P0ekt
The Attempt at a Solution
Taking the derivative of y, I get:
(Meaekt)*(aekt)*k
which is,
ky*aekt
..and I'm...
Homework Statement
The only functions with a constant doubling time are the exponential functions P0ekt with k > 0. Show that the doubling time of linear function f(t) = a(t) + b at time t0 is t0 + b/a.
Homework Equations
n/a
The Attempt at a Solution
With initial time t0, P = at0 + b
At...
Homework Statement
∫0-->x |t|dt
Homework Equations
//
The Attempt at a Solution
1/2*x^2 for x>= 0
1/2*(-x)^2 for x<= 0
Not sure what to do to be honest. (the answer in the back of the book says 1/2*x|x|).
Given that I am interested in both fields, which degree would give me the most job options after graduation (the degree is ECE, electrical and computer engineering)? For example, do employers consider applicants with an EE/CE (or in my case, ECE) degree when hiring software developers, or do...
Homework Statement
We want to make a conical drinking cup out of paper. It should hold exactly 100 cubic inches of water. Find the dimensions of a cup of this type that minimizes the surface area.
Homework Equations
SA = pi*r^2 + pi*r*l where l is the slant height of the cone.
V =...
Homework Statement
Find and prove the identity sec^-1(x) in terms of cos^-1(arg) (Note that 1/cos^-1(x) is not equal to sec^-1(x).
Homework Equations
None.
The Attempt at a Solution
sec(sec^-1(x)) = x
1/cos(sec^-1(x)) = x
1/cos(cos^-1(x)) = 1/x
1/cos(cos^-1(1/x)) = 1/1/x...
Homework Statement
Calculate the derivative with respect to x:
x/y + y/x = 2y
Homework Equations
n/a
The Attempt at a Solution
I end up getting the right answer, but what I want to know is how to isolate dy/dx to one side after implicitly differentiating. I have tried differentiating the...
Homework Statement
A particle moves counterclockwise around the ellipse with equation 9x^2 + 16y^2 = 25.
a). In which of the four quadrants in dx/dt > 0? Explain.
b). Find a relation between dx/dt and dy/dt.
c). At what rate is the x-coordinate changing when the particle passes the point...
Why is ln(e^x) =/= x?
The domain and range of the LHS are the same as the RHS, so I don't understand why this equation is false, where e^ln(x) = x, and the LHS and RHS of this does not have the same domain...
I know that e^x and ln(x) are inverse functions, so please don't only tell me this...
Homework Statement
compute the inverse derivative of f(x) = x^3/(x^2+1)
Homework Equations
n/a
The Attempt at a Solution
My issue is a purely algebraic one... getting the inverse function!
Attempting to solve for x yields no results!
y = x^3/(x^2+1)
y(x^2+1) = x^3
yx^2 + y = x^3
y = x^3 -...
Homework Statement
Which of the following satisfy (f^k)(x) = 0 for all k >= 6?
a) f(x) = 7x^4 + 4 + x^-1
b) f(x) = sqrt(x)
c) f(x) = x^(9/5)
d) f(x) = x^3 - 2
e) f(x) = 1 - x^6
f) f(x) = 2x^2 + 3x^5
Homework Equations
None, but given as a problem in a chapter where the topic is higher...
Homework Statement
Given the following formula for distance, find the average velocity on the interval [1,3]
S(t) = t/(1+t^2)
Homework Equations
Vavg = (S(t0) - S(t1)) / (t0 - t1)
or
Vavg = (V0 + V1)/2
The Attempt at a Solution
I get two different answers and I need help understand why...
Homework Statement
Using the definition of derivative find f'(x) for f(x) = x - sqrt(x)
Homework Equations
None.
The Attempt at a Solution
lim h --> 0 : ((x + h) - sqrt(x + h) - x + sqrt(x))/h
1 - (sqrt(x + h) - sqrt(x))/h
Multiply by conjugate..
1 - h/(h*(sqrt(x) +...
Homework Statement
I'm having trouble converting the LHS to the RHS of this equation:
http://www.wolframalpha.com/input/?i=%281%2F%28sqrt%285+%2B+h%29+%29-+1%2F%28sqrt%285%29%29%29%2Fh+%3D+-1%2F%28%28sqrt%285%29*sqrt%285%2Bh%29%29*%28sqrt%285%2Bh%29+%2B+sqrt%285%29%29%29
Homework Equations...
Homework Statement
Given a grid, x by y, where x and y are integers both greater than or equal to one, prove that it is impossible for there to be a point (a,b) where the distance d from (a,b) to three distinct corners of the grid are equal only for these three corners (i.e. the point has to...
By intro physics I mean calculus based Physics I (Newtonian physics).
I'm a freshman planning on majoring in CS and this is my first semester in college. I'm doing well in all my other courses, all A's (calc, intro to CS, others)... but physics, man.
I'm not kidding when I say, with a 5...