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Nairaland Forum / Nairaland / General / Education / CALCULUS: Please Help! Mathematicians In The House. (2225 Views)
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CALCULUS: Please Help! Mathematicians In The House. by PigMeat: 2:25pm On Nov 22, 2016 |
Greetings Mathematicians in the house. I have been having this difficulties in the problem below. Please help me out! Discontinuity and continuity of a function. X^2-81/x-9, (the square of X, minus 81, all over X-9) show that it is a removable continuous function. |
Re: CALCULUS: Please Help! Mathematicians In The House. by hammmedb: 2:31pm On Nov 22, 2016 |
Use quotient rule |
Re: CALCULUS: Please Help! Mathematicians In The House. by Gydion(m): 2:48pm On Nov 22, 2016 |
L'hopital rule will do it |
Re: CALCULUS: Please Help! Mathematicians In The House. by PigMeat: 2:59pm On Nov 22, 2016 |
hammmedb:Thanks for the suggestion bro, buh the problem is about continuity of a function, not the derivative. |
Re: CALCULUS: Please Help! Mathematicians In The House. by PigMeat: 3:00pm On Nov 22, 2016 |
Gydion:How bro? Please help me do it. |
Re: CALCULUS: Please Help! Mathematicians In The House. by NDSMELODY(m): 4:15pm On Nov 22, 2016 |
L'hopital rule wont work since we are not given any limit......firstly what is continuity of a function? |
Re: CALCULUS: Please Help! Mathematicians In The House. by NDSMELODY(m): 4:28pm On Nov 22, 2016 |
To the poster of the question you did not give us limit to work with,provided the limit is given just subtitute it into the function of x given,if the function of x is equal to 1 the function is said to be continous but if the function of x does not equal to 1 it is said to be discontinous function |
Re: CALCULUS: Please Help! Mathematicians In The House. by Gydion(m): 5:16pm On Nov 22, 2016 |
Snap the question and lemme solve it |
Re: CALCULUS: Please Help! Mathematicians In The House. by WalkerMichael(m): 5:18pm On Nov 22, 2016 |
Write down the question on a sheet of paper and snap then attach |
Re: CALCULUS: Please Help! Mathematicians In The House. by Efewestern: 6:22pm On Nov 22, 2016 |
Your question is not complete.. Snap it .. Also provide the limit. |
Re: CALCULUS: Please Help! Mathematicians In The House. by PigMeat: 6:50pm On Nov 22, 2016 |
NDSMELODY:From the question x approaches 9. Thanks for the correction. If I equate 9 for X it will be zero and discontinued. But they say show that it is a removable and a continuous function, thank. |
Re: CALCULUS: Please Help! Mathematicians In The House. by PigMeat: 7:00pm On Nov 22, 2016 |
Efewestern:Limits as X~>9 |
Re: CALCULUS: Please Help! Mathematicians In The House. by Efewestern: 7:23pm On Nov 22, 2016 |
PigMeat: okay, Let's do some mathematics.. You have X^2-81/ X - 9 = X^2 - 9^2/ X - 9 = (X - 9) (X + 9) / (X - 9)...... (1) = from eqn 1, (X-9) will stroke out the denominator (X - 9) so we are left with (X + 9) At lim x-> 9 X + 9 = 9 + 9 = 18. , Mathematicians in the house please correct me if am wrong.. we are all learning.. |
Re: CALCULUS: Please Help! Mathematicians In The House. by coobboy(m): 7:26pm On Nov 22, 2016 |
Lim x^2-81. (X-9)(x+9) -------- = ------------ X - 9 X-9 The x-9 cancels X--> 9 Lim x --> 9 (9+9) = 18 As x tends to 9 on x - 9 it's discontinuity is on 18 |
Re: CALCULUS: Please Help! Mathematicians In The House. by Efewestern: 7:29pm On Nov 22, 2016 |
coobboy: How is X infinite... ? |
Re: CALCULUS: Please Help! Mathematicians In The House. by coobboy(m): 7:30pm On Nov 22, 2016 |
Efewestern: It's a limit question as x goes to infinity |
Re: CALCULUS: Please Help! Mathematicians In The House. by PigMeat: 7:34pm On Nov 22, 2016 |
Efewestern: So the limit is continued at 18? |
Re: CALCULUS: Please Help! Mathematicians In The House. by Efewestern: 7:36pm On Nov 22, 2016 |
coobboy:X tends to 9 not infinity |
Re: CALCULUS: Please Help! Mathematicians In The House. by Efewestern: 7:39pm On Nov 22, 2016 |
PigMeat:No its discontinous.. When you solved it wat was your answer. ? |
Re: CALCULUS: Please Help! Mathematicians In The House. by PigMeat: 7:44pm On Nov 22, 2016 |
coobboy:The part B of the question said find the limit if it continous. |
Re: CALCULUS: Please Help! Mathematicians In The House. by firstclassmumu: 7:55pm On Nov 22, 2016 |
God give me brain na make me too fit contribute for dis kain tin. Una weldone oooo. I Know Even Know Where To Start From 4 Likes |
Re: CALCULUS: Please Help! Mathematicians In The House. by PigMeat: 8:56pm On Nov 22, 2016 |
Efewestern:I have not solved it. It a problem for me. U mean it is discontinued at 18? So what is the continuity in it? How do u go abt that? |
Re: CALCULUS: Please Help! Mathematicians In The House. by NDSMELODY(m): 10:34pm On Nov 22, 2016 |
Subtitute 9 in the equation we get 0/0 which is indeterminate ......9^2-81/9-9 = 0/0 now we can use l'hopital rule by differentiating the numerator and denominator of the function then we have 2x-0/1-0 = 2x then subtitute limit as x->9 which gives 18.........so the function f(x) is said to b discontinous since f(x) is not equal to 1. 1 Like |
Re: CALCULUS: Please Help! Mathematicians In The House. by Godwinfriz(m): 10:43pm On Nov 22, 2016 |
Thank god for mathematics hmm nw hw dis tin tak help pesin directly |
Re: CALCULUS: Please Help! Mathematicians In The House. by Sandydayziz(f): 11:00pm On Nov 22, 2016 |
Run outta thread** |
Re: CALCULUS: Please Help! Mathematicians In The House. by coobboy(m): 11:42pm On Nov 22, 2016 |
PigMeat: Okay that's even better The answer is 18 ---- lim x-->>9 (x+9) = (9+9) =18 |
Re: CALCULUS: Please Help! Mathematicians In The House. by Efewestern: 7:23am On Nov 23, 2016 |
coobboy: NDSMELODY: Exactly what I solved earlier, So we all arrive at 18 right ?.. meaning its discontinuos .... OP any more problem ? |
Re: CALCULUS: Please Help! Mathematicians In The House. by Efewestern: 7:28am On Nov 23, 2016 |
Sandydayziz: Godwinfriz: See them art students.. By there fruit we sha know dem firstclassmumu: Judging from your moniker I was thinking you gonna deliver .. , So which first class are we talking about now? |
Re: CALCULUS: Please Help! Mathematicians In The House. by firstclassmumu: 8:23am On Nov 23, 2016 |
Efewestern:are you talking to me? |
Re: CALCULUS: Please Help! Mathematicians In The House. by PigMeat: 9:34am On Nov 23, 2016 |
That you all @ cooboy ndsmelody efewestern y'all contributions were really helpful . Here is another question (1) Prove that limx~>0 (sinx/x)=1 (2) Evaluate limx~>0 (x^3+x^2/x^2) |
Re: CALCULUS: Please Help! Mathematicians In The House. by Efewestern: 10:31am On Nov 23, 2016 |
PigMeat: 2) We have lim X-> 0 (X^3 + X^2/ X^2) = X^3/X^2 + X^2/X^2 From indices = X^3-2 + X^2-2 = X^1 + X^0 Remember that anything to power zero is 1 , so we have = X^1 + 1 = lim X-> 0 0^1 + 1 = 0 + 1 = 1. that's ur final answer.. As for number 1, will solve it when am chance. bye. Correct me if am wrong oo.. nobody is perfect.. |
Re: CALCULUS: Please Help! Mathematicians In The House. by NDSMELODY(m): 1:41pm On Nov 23, 2016 |
Using l'hopital rule for the two question......1. Sinx/x subtitute x = 0 we get sin 0/0 = 0/0 which is indeterminate now by differentiating both numerator and denominator we get cosx/1 then subtitute x= 0 we get cos0/1 = 1/1 which gives 1 question 2. Subtitute x = 0 we have 0/0 which is indeterminate by finding the first derivative we have 3x^2 + 2x/2x subt x = 0 we get 0/0 again then find second derivative we get 6x+2/2 then subt x = 0 we get 2/2 which gives 1....... |
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