Calculus - limits: Help!

[emjee17]

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Guys, please try to help me with these limit problems:
@mods- ako lang gibutang diri sa gen.discussion arun mas dghan maka answer.

legend:
x^2 = x SQUARED

1. show that

lim x^2-1/x+1 = -2
x--> -1

2. prove that

lim (7-3x) = -2
x-->3

Thanks in advance. I will highly appreciate any answer/drafts.

[choc]

1.) (x+1)(x-1)/(x+1) = -2
x-1- = -2
-1-1 = -2

2.) 7-3(3) = -2
7 - 9 = -2

[mortal_bane]

1.) (x+1)(x-1)/(x+1) = -2
x-1- = -2
-1-1 = -2

2.) 7-3(3) = -2
7 - 9 = -2

gi answeran naman niya. pero sakto ni cya!

[emjee17]

^ i mean, amo mang gud answers kay ingon ani:


given example:

1. show that lim (4x-5) = 3
x--> 2

Proof: let E(epsilon) > 0.
Observe that: |(4x-5) - 3| = |4x-8|
= |4(x-2)|
= |4| |x-2|

Take d(delta)=E/4. Then, for all x E IR(all real nos.), such that
0<|x-2|<d, then
|(4x-5) - 3| = |4x-8|
= |4(x-2)|
= |4| |x-2|
< 4d = 4 E/4
Thus, |(4x-5) - 3| < E.
Therefore, by definition lim (4x-5) = 3.
x-->2

**ingon ani pag present sa among maestrong pwerting pagka paspasa mu discuss. tsk3.

[rAiNe_]

OT:
nagsunggo akong ilong.. as in im not good when it comes to this or when it's about solving problems like this.. murag makuyapan man ko kitag numbers ui.. basa mode lang ko, naa pa nya koy masabtan..

[etzina]

sis download this pdf and check out page 2... i forgot this naman so i searched google for it and found this: http://www.mathhelpforum.com/math-he...silondelta.pdf

[mortal_bane]

^ i mean, amo mang gud answers kay ingon ani:


given example:

1. show that lim (4x-5) = 3
x--> 2

Proof: let E(epsilon) > 0.
Observe that: |(4x-5) - 3| = |4x-8|
= |4(x-2)|
= |4| |x-2|

Take d(delta)=E/4. Then, for all x E IR(all real nos.), such that
0<|x-2|<d, then
|(4x-5) - 3| = |4x-8|
= |4(x-2)|
= |4| |x-2|
< 4d = 4 E/4
Thus, |(4x-5) - 3| < E.
Therefore, by definition lim (4x-5) = 3.
x-->2

**ingon ani pag present sa among maestrong pwerting pagka paspasa mu discuss. tsk3.

OT: Asa man diay ka nag skul?

[choc]

kakuti ba d i ani sis...gesubay man jud sa pamalaud..dugay napud ko la kagunit og libro,papel og bpen...
ambot tama ba ni...

legend: []=absolute sign


1. (x^2-1)/(x+1) = -2
(x+1)(x-1)/(x+1) = -2
x-1 = -2 ;
[x+2 = 0]
[x+2] = 0 ; consider the positive limit , thus E>0;

mao nga [x+2] < E
considering the Delta, using the limit x--> -2
x = -2
x + 2 = 0 , delta should be positive so delta>0
[x+2] < delta
compare ang E and delta;
[x+2]<E ; [x+2]<delta
[x+2]<E=delta
mao nga delta =(1/k)E , where k is a constant and in this case k is equal to 1...

.....hehehe..ambot tama ba ni, mao dili nalang nako esuwat ang no.2 kay basin mali ra japun og basin malibog rakag samot, kapoy2 type.

[kurdapia.nikki]

Emj, ayaw padala anang books ninyo nga lisud kaayu'g terms and symbols gigamit
Kasagaran old copyrights, confusing jud ang terms.

CHOC is right

[emjee17]

@rAine: hehe.. pariha rata.. XD

@ etzina: okie2. thanks for this.

@mortal_bane: san jose.

@choc: lagi oi. when i saw your answer: i was like WOW. ngun ani ra diay ka simple? sa among teacher, [calculus for business] makamatay ang iyang solutions. paspas pa jud kaayu mu discuss. commerce students sa san jose kay wala kaayu na kaagi ug fundamental math unlike engineering studs. ang amo is algebra ang quantitative analysis.

but anyway, you are definitely a great help. thanks for this. i'll be posting other problems. hehehe..

@kurdaps: hehe. bisag new books pa basta di maayu pagka discuss, di jud na masabtan..