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Help me with Calculus

 Posts: 391 Add as FriendChallenge to a DebateSend a Message 2/2/2014 11:11:55 AMPosted: 4 years agoIf your good at calculus can you show all your steps in working out the problem below.You can not use L'Hopitals rule because I'm not allowed to yet.What is the Limit of ( sin(x) / x - pi) as x goes to piShow all your steps thanks.
 Posts: 5,680 Add as FriendChallenge to a DebateSend a Message 2/2/2014 12:33:26 PMPosted: 4 years agoAt 2/2/2014 11:11:55 AM, Disquisition wrote:If your good at calculus can you show all your steps in working out the problem below.You can not use L'Hopitals rule because I'm not allowed to yet.What is the Limit of ( sin(x) / x - pi) as x goes to piShow all your steps thanks.is the (x-p) in the denominator, or is it: sin(x)/x - pi?30 Important Life Lessons http://www.debate.org... 20 Terrifying Two-Sentence Horrors http://www.debate.org... 20 Jokes That Only Geniuses Will Understand http://www.debate.org... Name One Song That Can't Match This GIF http://d24w6bsrhbeh9d.cloudfront.net...
 Posts: 391 Add as FriendChallenge to a DebateSend a Message 2/2/2014 12:39:46 PMPosted: 4 years agoAt 2/2/2014 12:33:26 PM, yay842 wrote:At 2/2/2014 11:11:55 AM, Disquisition wrote:If your good at calculus can you show all your steps in working out the problem below.You can not use L'Hopitals rule because I'm not allowed to yet.What is the Limit of ( sin(x) / x - pi) as x goes to piShow all your steps thanks.is the (x-p) in the denominator, or is it: sin(x)/x - pi?The (x -pi) is the denominator and sin(x) is the numerator.
 Posts: 391 Add as FriendChallenge to a DebateSend a Message 2/2/2014 12:46:04 PMPosted: 4 years agoAnd if anyone could also help me find the derivative off(x) = x^3 + 3x / x^2 -1 , so basically df/dx =?Use the quotient rule and show all your steps
 Posts: 6,675 Add as FriendChallenge to a DebateSend a Message 2/2/2014 12:49:28 PMPosted: 4 years agoAt 2/2/2014 12:46:04 PM, Disquisition wrote:And if anyone could also help me find the derivative off(x) = x^3 + 3x / x^2 -1 , so basically df/dx =?Use the quotient rule and show all your stepsIs x^2-1 the denominator? If so you should put it in parentheses.Stooge the Worst #StandWithBossy #UnbanTheCuntMan "bossy r u like 85 years old and have lost ur mind" ~mysteriouscrystals "I've honestly never seen seventh post anything that wasn't completely idiotic in a trying-to-be-funny way." ~F-16 "SeventhProfessor is actually a surprisingly good poster." ~Devilry https://docs.google.com...
 Posts: 5,680 Add as FriendChallenge to a DebateSend a Message 2/2/2014 12:59:28 PMPosted: 4 years agoAt 2/2/2014 12:39:46 PM, Disquisition wrote:At 2/2/2014 12:33:26 PM, yay842 wrote:At 2/2/2014 11:11:55 AM, Disquisition wrote:If your good at calculus can you show all your steps in working out the problem below.You can not use L'Hopitals rule because I'm not allowed to yet.What is the Limit of ( sin(x) / x - pi) as x goes to piShow all your steps thanks.is the (x-p) in the denominator, or is it: sin(x)/x - pi?The (x -pi) is the denominator and sin(x) is the numerator.i see no way of doing this one without lepitals rule but I guess you can move the (x-pi) to the numerator and do product rule30 Important Life Lessons http://www.debate.org... 20 Terrifying Two-Sentence Horrors http://www.debate.org... 20 Jokes That Only Geniuses Will Understand http://www.debate.org... Name One Song That Can't Match This GIF http://d24w6bsrhbeh9d.cloudfront.net...
 Posts: 1,172 Add as FriendChallenge to a DebateSend a Message 2/2/2014 1:02:21 PMPosted: 4 years agoAt 2/2/2014 11:11:55 AM, Disquisition wrote:If your good at calculus can you show all your steps in working out the problem below.You can not use L'Hopitals rule because I'm not allowed to yet.What is the Limit of ( sin(x) / x - pi) as x goes to piShow all your steps thanks.Limit sin (x)/ x-pix->piAs we know: Sin(x-pi)= sin(x)cos(pi) - sin(pi)cos(x)...................... = sinx(-1) - (0)cosx....................... = -sinx- 0 = -sinxHence Sin(x)= -sin (x-pi)Replacing this in LimitLimit -sin(x-pi)/ (x-pi)x->piTaking out (-1)(-1) Limit sin (x-pi)/ (x-pi)x->pi(-1) . (1)**By applying limit formula:Limit sin(y)/y = 1y->0= -1Is it ok?Remove the "I want", remainder is the "peace". ~Al-Ghazali~ "This time will also pass", a dose to cure both; the excitement & the grievance. ~Ayaz~
 Posts: 5,680 Add as FriendChallenge to a DebateSend a Message 2/2/2014 1:13:35 PMPosted: 4 years agof(x) = x^3 + 3x / x^2 -11. quotient rule: (vu'-uv')/v^22. [(x^2-1)(3x^2+3)-(x^3+3x)(2x)]/(x^2-1)^23. (3x^3+3x^2-3x-3-6x^3-6x)/(x^4-1)4. (-3x^3+3x^2-9x-3)/(x^4-1)5. if you want to simplify it further: 3(-x^3+x^2-3x-1)/(x^4-1)DONE30 Important Life Lessons http://www.debate.org... 20 Terrifying Two-Sentence Horrors http://www.debate.org... 20 Jokes That Only Geniuses Will Understand http://www.debate.org... Name One Song That Can't Match This GIF http://d24w6bsrhbeh9d.cloudfront.net...
 Posts: 1,172 Add as FriendChallenge to a DebateSend a Message 2/2/2014 1:16:53 PMPosted: 4 years agoAt 2/2/2014 12:46:04 PM, Disquisition wrote:And if anyone could also help me find the derivative off(x) = x^3 + 3x / x^2 -1 , so basically df/dx =?Use the quotient rule and show all your stepsf(x)= x^3 + 3x /(x^2-1)Quotient Ruledy/dx = [(x^2-1)(3x^2+3)-(x^3+3x)(2x)] / {(x^2-1)^2}= Solve the algebra to simplify.Remove the "I want", remainder is the "peace". ~Al-Ghazali~ "This time will also pass", a dose to cure both; the excitement & the grievance. ~Ayaz~
 Posts: 5,680 Add as FriendChallenge to a DebateSend a Message 2/2/2014 1:32:31 PMPosted: 4 years agoAt 2/2/2014 1:16:53 PM, Dazz wrote:At 2/2/2014 12:46:04 PM, Disquisition wrote:And if anyone could also help me find the derivative off(x) = x^3 + 3x / x^2 -1 , so basically df/dx =?Use the quotient rule and show all your stepsf(x)= x^3 + 3x /(x^2-1)Quotient Ruledy/dx = [(x^2-1)(3x^2+3)-(x^3+3x)(2x)] / {(x^2-1)^2}= Solve the algebra to simplify.beat you to it already, try solving the 1st one without lepital's rule(which i dont see how)30 Important Life Lessons http://www.debate.org... 20 Terrifying Two-Sentence Horrors http://www.debate.org... 20 Jokes That Only Geniuses Will Understand http://www.debate.org... Name One Song That Can't Match This GIF http://d24w6bsrhbeh9d.cloudfront.net...
 Posts: 2,052 Add as FriendChallenge to a DebateSend a Message 2/2/2014 1:49:44 PMPosted: 4 years agoYay, I get a different answer:f(x) = ( x^3 + 3x ) / ( x^2 -1 )f(x)' = ?1. quotient rule: (vu'-uv')/v^22. [ ( x^2 - 1 ) ( 3x^2 + 3 ) - ( x^3 + 3x ) ( 2x ) ] / ( x^2 - 1 ) ^23. ( x^4 - 6x^2 - 3 ) / [ ( x^2 - ) ( x^2 - 1 ) ]4. ( x^4 - 6x^2 - 3 ) / ( x^4 - 2x^2 + 1 )Step 4 is the answer.
 Posts: 2,052 Add as FriendChallenge to a DebateSend a Message 2/2/2014 1:54:37 PMPosted: 4 years agoStep 3 should read ( x^4 - 6x^2 - 3 ) / [ ( x^2 - 1 ) ( x^2 - 1 ) ]I did it twice and I still get the same answer I got in Step 4.
 Posts: 5,680 Add as FriendChallenge to a DebateSend a Message 2/2/2014 1:56:23 PMPosted: 4 years agoAt 2/2/2014 1:49:44 PM, Juan_Pablo wrote:Yay, I get a different answer:f(x) = ( x^3 + 3x ) / ( x^2 -1 )f(x)' = ?1. quotient rule: (vu'-uv')/v^22. [ ( x^2 - 1 ) ( 3x^2 + 3 ) - ( x^3 + 3x ) ( 2x ) ] / ( x^2 - 1 ) ^23. ( x^4 - 6x^2 - 3 ) / [ ( x^2 - ) ( x^2 - 1 ) ]4. ( x^4 - 6x^2 - 3 ) / ( x^4 - 2x^2 + 1 )Step 4 is the answer.you screwed up 2 to 3. there is no power to the 4 in in the numerator30 Important Life Lessons http://www.debate.org... 20 Terrifying Two-Sentence Horrors http://www.debate.org... 20 Jokes That Only Geniuses Will Understand http://www.debate.org... Name One Song That Can't Match This GIF http://d24w6bsrhbeh9d.cloudfront.net...
 Posts: 5,680 Add as FriendChallenge to a DebateSend a Message 2/2/2014 1:58:01 PMPosted: 4 years agoAt 2/2/2014 11:11:55 AM, Disquisition wrote:If your good at calculus can you show all your steps in working out the problem below.You can not use L'Hopitals rule because I'm not allowed to yet.What is the Limit of ( sin(x) / x - pi) as x goes to piShow all your steps thanks.well i see no way to do this with lepitals ruel, but just to show you:1. derivative of sinx = cosx2. derivative of x - pi = 13. cos pi = 14. the limit as x approaches pi of (sin(x))/(x-pi)=130 Important Life Lessons http://www.debate.org... 20 Terrifying Two-Sentence Horrors http://www.debate.org... 20 Jokes That Only Geniuses Will Understand http://www.debate.org... Name One Song That Can't Match This GIF http://d24w6bsrhbeh9d.cloudfront.net...
 Posts: 5,680 Add as FriendChallenge to a DebateSend a Message 2/2/2014 1:59:01 PMPosted: 4 years agoAt 2/2/2014 1:54:37 PM, Juan_Pablo wrote:Step 3 should read ( x^4 - 6x^2 - 3 ) / [ ( x^2 - 1 ) ( x^2 - 1 ) ]I did it twice and I still get the same answer I got in Step 4.nvm i take that back, there is a power to the fourth30 Important Life Lessons http://www.debate.org... 20 Terrifying Two-Sentence Horrors http://www.debate.org... 20 Jokes That Only Geniuses Will Understand http://www.debate.org... Name One Song That Can't Match This GIF http://d24w6bsrhbeh9d.cloudfront.net...
 Posts: 5,680 Add as FriendChallenge to a DebateSend a Message 2/2/2014 1:59:53 PMPosted: 4 years agoi cant tell sh*t in this format, i gots to right it down30 Important Life Lessons http://www.debate.org... 20 Terrifying Two-Sentence Horrors http://www.debate.org... 20 Jokes That Only Geniuses Will Understand http://www.debate.org... Name One Song That Can't Match This GIF http://d24w6bsrhbeh9d.cloudfront.net...
 Posts: 2,052 Add as FriendChallenge to a DebateSend a Message 2/2/2014 2:05:23 PMPosted: 4 years agoStep 2 to 3:[ ( x^2 - 1 ) ( 3x^2 + 3 ) - ( x^3 + 3x ) ( 2x ) ] / ( x^2 - 1 ) ^2 =[ ( 3x^4 + 3x^2 - 3x^2 - 3 ) + ( -2x^4 - 6x^2 ) ] / [ ( x^2 - 1 ) ( x^2 - 1 ) ]Step 3: ( x^4 - 6x^2 - 3 ) / [ ( x^2 - ) ( x^2 - 1 ) ]I still get the same answer. You made a mistake somewhere.It's okay, Yay. I frequently make similar mistakes and have to re-check my answers too. ;)
 Posts: 2,052 Add as FriendChallenge to a DebateSend a Message 2/2/2014 2:07:12 PMPosted: 4 years agoSince I'm going to be an integrative science teacher, it's good for me to practice this stuff. :))
 Posts: 5,680 Add as FriendChallenge to a DebateSend a Message 2/2/2014 2:14:04 PMPosted: 4 years agoAt 2/2/2014 2:05:23 PM, Juan_Pablo wrote:Step 2 to 3:[ ( x^2 - 1 ) ( 3x^2 + 3 ) - ( x^3 + 3x ) ( 2x ) ] / ( x^2 - 1 ) ^2 =[ ( 3x^4 + 3x^2 - 3x^2 - 3 ) + ( -2x^4 - 6x^2 ) ] / [ ( x^2 - 1 ) ( x^2 - 1 ) ]Step 3: ( x^4 - 6x^2 - 3 ) / [ ( x^2 - ) ( x^2 - 1 ) ]I still get the same answer. You made a mistake somewhere.It's okay, Yay. I frequently make similar mistakes and have to re-check my answers too. ;)http://thesamerainbowsend.com...30 Important Life Lessons http://www.debate.org... 20 Terrifying Two-Sentence Horrors http://www.debate.org... 20 Jokes That Only Geniuses Will Understand http://www.debate.org... Name One Song That Can't Match This GIF http://d24w6bsrhbeh9d.cloudfront.net...
 Posts: 391 Add as FriendChallenge to a DebateSend a Message 2/2/2014 2:24:22 PMPosted: 4 years agoAt 2/2/2014 2:05:23 PM, Juan_Pablo wrote:Step 2 to 3:[ ( x^2 - 1 ) ( 3x^2 + 3 ) - ( x^3 + 3x ) ( 2x ) ] / ( x^2 - 1 ) ^2 =[ ( 3x^4 + 3x^2 - 3x^2 - 3 ) + ( -2x^4 - 6x^2 ) ] / [ ( x^2 - 1 ) ( x^2 - 1 ) ]Step 3: ( x^4 - 6x^2 - 3 ) / [ ( x^2 - ) ( x^2 - 1 ) ]I still get the same answer. You made a mistake somewhere.It's okay, Yay. I frequently make similar mistakes and have to re-check my answers too. ;)Thanks I forgot to expand (x^2-1) to (x-1)(x+1) and multiply separately. After that I got the same answer you did.
 Posts: 391 Add as FriendChallenge to a DebateSend a Message 2/2/2014 2:25:49 PMPosted: 4 years agoAt 2/2/2014 1:02:21 PM, Dazz wrote:At 2/2/2014 11:11:55 AM, Disquisition wrote:If your good at calculus can you show all your steps in working out the problem below.You can not use L'Hopitals rule because I'm not allowed to yet.What is the Limit of ( sin(x) / x - pi) as x goes to piShow all your steps thanks.Limit sin (x)/ x-pix->piAs we know: Sin(x-pi)= sin(x)cos(pi) - sin(pi)cos(x)...................... = sinx(-1) - (0)cosx....................... = -sinx- 0 = -sinxHence Sin(x)= -sin (x-pi)Replacing this in LimitLimit -sin(x-pi)/ (x-pi)x->piTaking out (-1)(-1) Limit sin (x-pi)/ (x-pi)x->pi(-1) . (1)**By applying limit formula:Limit sin(y)/y = 1y->0= -1Is it ok?I get everything until you get to the limit formula part. Could you elaborate on that, since I just started Cal 1
 Posts: 2,052 Add as FriendChallenge to a DebateSend a Message 2/2/2014 2:27:00 PMPosted: 4 years agoAt 2/2/2014 2:24:22 PM, Disquisition wrote:At 2/2/2014 2:05:23 PM, Juan_Pablo wrote:Step 2 to 3:[ ( x^2 - 1 ) ( 3x^2 + 3 ) - ( x^3 + 3x ) ( 2x ) ] / ( x^2 - 1 ) ^2 =[ ( 3x^4 + 3x^2 - 3x^2 - 3 ) + ( -2x^4 - 6x^2 ) ] / [ ( x^2 - 1 ) ( x^2 - 1 ) ]Step 3: ( x^4 - 6x^2 - 3 ) / [ ( x^2 - ) ( x^2 - 1 ) ]I still get the same answer. You made a mistake somewhere.It's okay, Yay. I frequently make similar mistakes and have to re-check my answers too. ;)Thanks I forgot to expand (x^2-1) to (x-1)(x+1) and multiply separately. After that I got the same answer you did.No problem, Diquisition.
 Posts: 2,052 Add as FriendChallenge to a DebateSend a Message 2/2/2014 2:48:42 PMPosted: 4 years agoBy the way, Disquisition, for you first problem you can't use L'Hospital's rule.The problem isn't of the indeterminate form[ lim x->a f (x) ] / [ lim x->a g (x) ] = 0 / 0 or infinity / inifinity.L'Hospital's rules doesn't apply.
 Posts: 2,052 Add as FriendChallenge to a DebateSend a Message 2/2/2014 2:50:18 PMPosted: 4 years agoYou're going to have to find some other method to find the limit of the problem as x->pi.
 Posts: 391 Add as FriendChallenge to a DebateSend a Message 2/2/2014 2:50:20 PMPosted: 4 years agoAt 2/2/2014 2:27:00 PM, Juan_Pablo wrote:No problem, Diquisition.Here is another one if your up to it.What is the derivative of f(x) = cos(2x), when c = (pi) / (4),The question basically wants us to plug it into this equation [f ( c+h ) - f ( c )] / hso I think its saying to determine the derivative of cos(2x) when x = (pi) / (4)
 Posts: 5,680 Add as FriendChallenge to a DebateSend a Message 2/2/2014 2:57:05 PMPosted: 4 years agoAt 2/2/2014 2:48:42 PM, Juan_Pablo wrote:By the way, Disquisition, for you first problem you can't use L'Hospital's rule.The problem isn't of the indeterminate form[ lim x->a f (x) ] / [ lim x->a g (x) ] = 0 / 0 or infinity / inifinity.L'Hospital's rules doesn't apply.its not indeterminate?30 Important Life Lessons http://www.debate.org... 20 Terrifying Two-Sentence Horrors http://www.debate.org... 20 Jokes That Only Geniuses Will Understand http://www.debate.org... Name One Song That Can't Match This GIF http://d24w6bsrhbeh9d.cloudfront.net...
 Posts: 5,680 Add as FriendChallenge to a DebateSend a Message 2/2/2014 2:59:00 PMPosted: 4 years agoAt 2/2/2014 2:50:20 PM, Disquisition wrote:At 2/2/2014 2:27:00 PM, Juan_Pablo wrote:No problem, Diquisition.Here is another one if your up to it.What is the derivative of f(x) = cos(2x), when c = (pi) / (4),The question basically wants us to plug it into this equation [f ( c+h ) - f ( c )] / hso I think its saying to determine the derivative of cos(2x) when x = (pi) / (4)1. cos(2x), x=pi/42. derive: -2sin(2x)3. -2sine(2pi/4)4. -2sin(pi/2)=1 x -2 = -230 Important Life Lessons http://www.debate.org... 20 Terrifying Two-Sentence Horrors http://www.debate.org... 20 Jokes That Only Geniuses Will Understand http://www.debate.org... Name One Song That Can't Match This GIF http://d24w6bsrhbeh9d.cloudfront.net...
 Posts: 2,052 Add as FriendChallenge to a DebateSend a Message 2/2/2014 3:03:29 PMPosted: 4 years agoAt 2/2/2014 2:57:05 PM, yay842 wrote:At 2/2/2014 2:48:42 PM, Juan_Pablo wrote:By the way, Disquisition, for you first problem you can't use L'Hospital's rule.The problem isn't of the indeterminate form[ lim x->a f (x) ] / [ lim x->a g (x) ] = 0 / 0 or infinity / inifinity.L'Hospital's rules doesn't apply.its not indeterminate?It's not of an indeterminant form so that L'Hospital's rule can be used. The reason is that the lim sin(x) as x -> pi is neither 0 or infinity. Both the limits of the expression in the numerator and the denominator need equal 0 xor infinity.
 Posts: 391 Add as FriendChallenge to a DebateSend a Message 2/2/2014 3:24:27 PMPosted: 4 years agoAt 2/2/2014 2:59:00 PM, yay842 wrote:At 2/2/2014 2:50:20 PM, Disquisition wrote:At 2/2/2014 2:27:00 PM, Juan_Pablo wrote:No problem, Diquisition.Here is another one if your up to it.What is the derivative of f(x) = cos(2x), when c = (pi) / (4),The question basically wants us to plug it into this equation [f ( c+h ) - f ( c )] / hso I think its saying to determine the derivative of cos(2x) when x = (pi) / (4)1. cos(2x), x=pi/42. derive: -2sin(2x)3. -2sine(2pi/4)4. -2sin(pi/2)=1 x -2 = -2We haven't come to the point where we can use derivations of trig functions so I have to plug into formula :( but thanks anyways.
 Posts: 2,052 Add as FriendChallenge to a DebateSend a Message 2/2/2014 3:25:52 PMPosted: 4 years agoAt 2/2/2014 2:59:00 PM, yay842 wrote:At 2/2/2014 2:50:20 PM, Disquisition wrote:At 2/2/2014 2:27:00 PM, Juan_Pablo wrote:No problem, Diquisition.Here is another one if your up to it.What is the derivative of f(x) = cos(2x), when c = (pi) / (4),The question basically wants us to plug it into this equation [f ( c+h ) - f ( c )] / hso I think its saying to determine the derivative of cos(2x) when x = (pi) / (4)1. cos(2x), x=pi/42. derive: -2sin(2x)3. -2sine(2pi/4)4. -2sin(pi/2)=1 x -2 = -2Yay, I get a different answer. I get:1. cos ( 2x), x = pi / 42. [ cos ( 2x) ]' = - 2 sin ( 2 x )3. - 2 sin ( 2 pi / 4 )4. - 2 sin ( pi / 2 )5. -1.972588That can probably be cleanly restated with pi as a factor.
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