L'hopitals Rule

Given: ^4] Where is measured in meters, T is the temperature in kelvins, k is Boltzmann's constant. The Rayleigh-Jeans Law agrees with experimental measurements for long wavelengths but disagrees drastically for short wavelengths. [The law predicts that as but experiments have shown that.] This fact is known as the ultravi ...continues

Taylor polynomials

Use a taylor polynomial to show that , for a large wavelength, Planck's Law gives approximately the same values as the Rayleigh-Jeans Law. see the attached problem #2

Graphing 1

1. Use a Taylor polynomial to show that, for large wavelengths, Planck's Law gives approximately the same values as the Rayleigh-Jeans Law. 2. Graph f as given by both laws in the same screen and comment on the similarities and differences. Use T= 5700K ( the temperature of the Sun). ( you may want to change from meters to t ...continues

Graph

Investigate how the graph of changes as T varies. (use Planck's Law.) In particular, graph for the stars Betelgeuse (T=3400 K), Procyon (T= 6400K), and Sirius( T= 9200K) as well as the Sun. How dose the total radiation emitted (the are under the curve) vary with T? Use the graph to comment on why Sirius is known as a blue star ...continues

Related Rates word problem

A highway patrol helicopter hovers 3/10 mile above a level, straight interstate highway which has a posted speed limit of 65 miles per hour. The helicopter pilot sees a car on the highway and determines with radar that at that particular instant, the distance between the helicopter and the car is 1/2 mile and is increasing at a ...continues

Finding the sum of a geometric series.

Find the sum: 1/8+1/4+1/2+1+........64

Factoring and simplifying trigonometric expressions.

1. Simplify: sin^2(x)/sec^2(x)-1 2. Factor and simplify: cos^2(x)-sin^2(x)cos^2(x) 3. Perform the addition and simplify: 1/1+sinx + 1/1-sinx 4. Simplify: sec^4(x) + sec^2(x)-2

Finding the rate of change.

A series of swells passes through a group of surfers. They notice that for a few minutes, the waves pass through at regular intervals: every 14 seconds. Let t=0 be the time when the wave is at its lowest point. The maximum instantaneous increase in height of the wave is 2.25 feet per second. a. Find r(t), the rate of chang ...continues

Rate of change

Ichiro hits the ball and runs toward first base with a speed of 25 feet per second. The shortstop, who is exactly 40 feet in from third base on the baseline, gets the ball exactly 1.7 seconds after Ichiro started running (assume he runs at a constant rate.) At what rate is Ichiro's distance to the shortstop increasing at the m ...continues

Trapezoidal Rule and Simpson's Rule - Error analysis

I am working on Trapezoidal Rule and Simpson's Rule - Error analysis, but need to make sure I do them correctly. Since there are many potential sources of error, please work the problems showing ALL the steps.