Homework Statement
Series is:
(ln x)^n, n goes from 1 to infinity
Homework Equations
The Attempt at a Solution
For other problems I've seen the ratio test used to find the radius of convergence, but I don't think this can work here. What other things can I do to find where this...
Hey all, I am really struggling to understand this chapter about series. These are a few problems about convergence and divergence, and I'll probably have some questions about Taylor and maclaurin series when I do those problems too.
Homework Statement
1. Determine whether the sequence is...
Homework Statement
Test the series for convergence or divergence using the Alternating Series test:
1. sum of (-1)^n * n/(ln n)
2. sum of [sin(n*pi/2)]/n!
Homework Equations
The Attempt at a Solution
1. lim of n/(ln n) goes to infinity (as n->infinity), so it can't satisfy the...
Homework Statement
1. How many beats will be heard if two identical flutes each try to play middle C (262 Hz), but one is at 0.0 deg C and the other is at 20.0 deg C?
2. Two loudspeakers are 2.5 m apart. A person stands 3.0 m from one speaker and 3.5 m from the other. a) What is the lowest...
Homework Statement
1. An unfingered guitar string is 0.70 m long and is tuned to play E above middle C (330 Hz). How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?
2. An organ is in tune at 20 degrees C. By what fraction will the frequency be...
Homework Statement
a) For what nonzero values of k does the function y = sin kt satisfy the differential equation y" + 9y = 0?
b) For those values of k, verify that every member of the family of functions y = A*sin kt + B*cos kt is also a solution.
Homework Equations
The Attempt at...
I have a quiz coming up that includes this, so thanks for any help.
Homework Statement
A trough is filled with a liquid of density 840 kg/m^3. The ends of the trough are equilateral triangles with sides 8 m long and vertex at the bottom. Find the hydrostatic force on one end of the trough...
Thanks. Can you quickly check if I did this right:
\displaystyle{\int_{0}^{5} 62.5y(2 \sqrt{100-y}) \;dy}
\displaystyle{125 \int_{0}^{5} y \sqrt{100-y} \;dy}
Substituting u=100-y, du=-dy:
\displaystyle{-125 \int_{100}^{95} (u+100) \sqrt{u} \;du}
I get the answer to be 1218880 lb for...
Yes, the end of the tank is a semicircle. Looking at a similar example in the book, is the length of each strip 2 \sqrt{100-y_i^2}? Because in the book's example, the end of the tank is a full circle with radius 3, and they got the length of each strip to be 2 \sqrt{9-y_i^2}. I'm not sure how to...
Homework Statement
The end of a tank containing water is vertical and has the indicated shape (in attached picture). Explain how to approximate the hydrostatic force against the end of the tank by a Riemann sum. Then express the force as an integral and evaluate it.
Homework Equations...
Thanks mjsd.
I ran into another problem I'm having trouble with, this time with:
x=e^2y, 0<=y<=1/2 rotated about y-axis.
So, the integral is:
\displaystyle{2\pi \int_{0}^{1/2} y \sqrt{1 + 4e^{4y}} \;dx}
Here I don't think I can use trig substitutions because I can't get rid of the e. Thanks...
Homework Statement
Find the area of the surface obtained by rotating the curve about the x-axis:
y=cos 2x, 0<=x<=pi/6
Homework Equations
Surface area about the x-axis = Integral of 2pi * f(x) * sqrt(1+[f'(x)]^2) dx
The Attempt at a Solution
I think I set up my integral correctly, so...
1. A 160 cm tall person lies on a light (massless) board which is supported by two scales, one under the feet and one beneath the top of the head. The scale under the feet reads 29.4 kg and the one under the head reads 32.8 kg. Where is the center of gravity of this person measured from the...
Sorry for so many questions, I'm just trying to understand everything before my test coming up soon.
1. Let R be the region in the first quadrant under the graph of y=1/sqrt(x) for
4<=x<=9.
a) If the line x=k divides the region R into two regions of equal area, what is the value of k?
My...