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1. I'm trying to find the limit as theta approaches 0 of (1 - cos theta)/(2 sin^2 theta). Direct substitution yields an indeterminate form, so I did the following:
= 1/2 lim as theta approaches 0 of (1 - cos theta)/(1 - cos^2 theta)
Then I did something pretty sketchy involving taking the reciprocal of what I was finding the limit of so that I could get it into a form of the derivative, and then I tried doing something different a second time, but it's hardly worth transcribing all my erroneous work—can anyone point me in the right direction? The right answer is given as 1/4, but I'm having a hell of a time getting there.
2. If f(x) = sin x/2, then there exists a number c in the interval π/2 < x < 3π/2 that satisfies the conclusion for the Mean Value Theorem. I have to find a possible value for c. I tried plugging into the formula f'(c) = (f(b) - f(a))/(b - a), but that just gave me 0, since the numerator = sin 3π/4 - sin π/4 = 0. But apparently the answer is π. I can see that π = 2π/2, the mean of π/2 and 3π/2, but I thought the Mean Value Theorem had more to do with the formula I gave ... again, any help is much appreciated ... thanks, anon. —Preceding unsigned comment added by 70.19.22.49 ( talk) 00:19, 17 January 2008 (UTC)
Dear Wikipedia, I am faced with a math problem and you help would be much appreciated, thanks.
y=2^(-x+3) y=(1/8)(1/(x+2))+9
Intersection, therefore y=y, solve for x.
2^(-x+3)=(1/8)(1/(x+2))+9, Note: there ARE two real solutions.
LS: 2^(-x+3) RS:(1/8)(1/(x+2))+9
8*2^(-x) 1/(8x+16)+9 1/(8x+16)+(9(8x+16)/(8x+16) 1/(8x+16)+(72x+144)/(8x+16) (1+72x+144)/(8x+16) (72x+145)/(8x+16)
Combine 8*2^(-x)=(72x+145)/(8x+16) 8*2^(-x)=(72x+145)/(8(x+2) multiply both sides by 8 2^6*2^(-x)=(72x+145)/(x+2) simplify 2^(6-x)=(72x+145)/(x+2) multiply both sides by (x+2) (x+2)(2^(6-x))=72x+145 2x^(-x+6) + 2^(-x+7)-72x=145 and I'm stuck... please help, what is next step? did i mess up along the way? thanks —Preceding unsigned comment added by 99.241.96.136 ( talk) 02:55, 17 January 2008 (UTC)
Put the equation on the form f(x)=0, rather than on the form LS(x)=RS(x). Your result 8·2−x=(72·x+145)/(8·x+16) leads to the equation f(x)=0 where f is defined by f(x)=(72·x+145)·(2x)−64·x−128. In addition to the two solutions given above by Lambiam and Meni Rosenfeld, there are also an infinite number of non-real complex solutions. Substitute 2x=ex·ln(2) and use the power series for the exponential function to obtain polynomial approximations to f(x). Solve the corresponding equations using the Durand-Kerner method. Bo Jacoby ( talk) 22:08, 18 January 2008 (UTC).
What is 4.8 miles/second in metric? —Preceding unsigned comment added by 67.58.207.35 ( talk) 04:37, 17 January 2008 (UTC)
Metric what? 4.8 (miles per second) = 7.7248512 kilometers per second. You can do this with google. 70.162.25.53 ( talk) 04:45, 17 January 2008 (UTC)
My [
Sharp EL-506V], when calculating 3.5 x 7.6x10^-14 7.6x10^-10 displays the answer 0.000000002 BUT the actual answer is 2.66x10^-9 so it should say exactly that and at the very least, it should round properly and give 0.000000003 (still not acceptable in my opinion). Please check the output of your favourite calculator and enlighten me. :) ----
Seans
Potato Business
17:27, 17 January 2008 (UTC)
Mathematics desk | ||
---|---|---|
< January 16 | << Dec | January | Feb >> | January 18 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
1. I'm trying to find the limit as theta approaches 0 of (1 - cos theta)/(2 sin^2 theta). Direct substitution yields an indeterminate form, so I did the following:
= 1/2 lim as theta approaches 0 of (1 - cos theta)/(1 - cos^2 theta)
Then I did something pretty sketchy involving taking the reciprocal of what I was finding the limit of so that I could get it into a form of the derivative, and then I tried doing something different a second time, but it's hardly worth transcribing all my erroneous work—can anyone point me in the right direction? The right answer is given as 1/4, but I'm having a hell of a time getting there.
2. If f(x) = sin x/2, then there exists a number c in the interval π/2 < x < 3π/2 that satisfies the conclusion for the Mean Value Theorem. I have to find a possible value for c. I tried plugging into the formula f'(c) = (f(b) - f(a))/(b - a), but that just gave me 0, since the numerator = sin 3π/4 - sin π/4 = 0. But apparently the answer is π. I can see that π = 2π/2, the mean of π/2 and 3π/2, but I thought the Mean Value Theorem had more to do with the formula I gave ... again, any help is much appreciated ... thanks, anon. —Preceding unsigned comment added by 70.19.22.49 ( talk) 00:19, 17 January 2008 (UTC)
Dear Wikipedia, I am faced with a math problem and you help would be much appreciated, thanks.
y=2^(-x+3) y=(1/8)(1/(x+2))+9
Intersection, therefore y=y, solve for x.
2^(-x+3)=(1/8)(1/(x+2))+9, Note: there ARE two real solutions.
LS: 2^(-x+3) RS:(1/8)(1/(x+2))+9
8*2^(-x) 1/(8x+16)+9 1/(8x+16)+(9(8x+16)/(8x+16) 1/(8x+16)+(72x+144)/(8x+16) (1+72x+144)/(8x+16) (72x+145)/(8x+16)
Combine 8*2^(-x)=(72x+145)/(8x+16) 8*2^(-x)=(72x+145)/(8(x+2) multiply both sides by 8 2^6*2^(-x)=(72x+145)/(x+2) simplify 2^(6-x)=(72x+145)/(x+2) multiply both sides by (x+2) (x+2)(2^(6-x))=72x+145 2x^(-x+6) + 2^(-x+7)-72x=145 and I'm stuck... please help, what is next step? did i mess up along the way? thanks —Preceding unsigned comment added by 99.241.96.136 ( talk) 02:55, 17 January 2008 (UTC)
Put the equation on the form f(x)=0, rather than on the form LS(x)=RS(x). Your result 8·2−x=(72·x+145)/(8·x+16) leads to the equation f(x)=0 where f is defined by f(x)=(72·x+145)·(2x)−64·x−128. In addition to the two solutions given above by Lambiam and Meni Rosenfeld, there are also an infinite number of non-real complex solutions. Substitute 2x=ex·ln(2) and use the power series for the exponential function to obtain polynomial approximations to f(x). Solve the corresponding equations using the Durand-Kerner method. Bo Jacoby ( talk) 22:08, 18 January 2008 (UTC).
What is 4.8 miles/second in metric? —Preceding unsigned comment added by 67.58.207.35 ( talk) 04:37, 17 January 2008 (UTC)
Metric what? 4.8 (miles per second) = 7.7248512 kilometers per second. You can do this with google. 70.162.25.53 ( talk) 04:45, 17 January 2008 (UTC)
My [
Sharp EL-506V], when calculating 3.5 x 7.6x10^-14 7.6x10^-10 displays the answer 0.000000002 BUT the actual answer is 2.66x10^-9 so it should say exactly that and at the very least, it should round properly and give 0.000000003 (still not acceptable in my opinion). Please check the output of your favourite calculator and enlighten me. :) ----
Seans
Potato Business
17:27, 17 January 2008 (UTC)