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      09-10-2013, 11:58 AM   #1
bumere90
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Calculus I problem

Anyone good in Calculus?
I solved the problem, but I am not sure if I am correct or not.

The problem states:
Discuss the continuity of f(x)= (x^2+2x-3)/(x+3) on interval [-5, 2]

Since polynomials are continuous everywhere, this particular function is not defined at x=-3.
Do i just state that the function is continuous everywhere except at x=-3 ?
Do I have to find one sided limits as well?

f(-5)= {(-5)^2+2(-5)-3)}/{(2+3)}= -6

f(2) = {(2)^2+2(2)-3)}/{(2+3)} = 1

lim
x->-5+ so I find the limit from the right side and get = -6

lim
x->2- and I get = 1

since, my function values equal the limits...does it say the function is continuous everywhere except at x=-3?
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      09-10-2013, 12:37 PM   #2
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EDIT- I'm wrong

EDIT 2-

the limit exists when -5<x<-3 and -3<x<2

The limit is defined -6<f(x)<0 and 0<f(x)<1

discontinuity when x=-3

let's go with that.

Last edited by RandomHero; 09-10-2013 at 01:12 PM.
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      09-10-2013, 01:38 PM   #3
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I remember when I took Calculus I back in senior year of high school. I forgot everything.
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      09-10-2013, 01:42 PM   #4
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      09-10-2013, 02:02 PM   #5
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Quote:
Originally Posted by KingOfJericho View Post
After 10 years at a major financial institution, I can confirm that this will never be used in your real life.
After a year of working as an engineer I can also confirm that this will not be needed. With that being said, I forgot everything from Calc I. Sorry
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      09-10-2013, 02:20 PM   #6
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Quote:
Originally Posted by bumere90 View Post
Anyone good in Calculus?
I solved the problem, but I am not sure if I am correct or not.

The problem states:
Discuss the continuity of f(x)= (x^2+2x-3)/(x+3) on interval [-5, 2]

Since polynomials are continuous everywhere, this particular function is not defined at x=-3.
Do i just state that the function is continuous everywhere except at x=-3 ?
Do I have to find one sided limits as well?

f(-5)= {(-5)^2+2(-5)-3)}/{(2+3)}= -6

f(2) = {(2)^2+2(2)-3)}/{(2+3)} = 1

lim
x->-5+ so I find the limit from the right side and get = -6

lim
x->2- and I get = 1

since, my function values equal the limits...does it say the function is continuous everywhere except at x=-3?
Yes, you have to use the range notation to exclude -3.
Example [-Infinity to -4] [-2 to +Infinity]
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      09-10-2013, 02:24 PM   #7
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Also, this information maybe needed later in life. For example i never really paid attention in Trigonometry class.

Until recently, i had to write a function that involved trig and calc. I did some personal research and I thought my self much better than i learned in school.
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      09-10-2013, 02:42 PM   #8
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You would simply state that the function is continuous over the ranges [-5,-3) and (-3,2]. More generally, the function is continuous everywhere except for x=-3 as you stated, which can formally be written as continuous over the ranges (-Inf,-3) and (-3,+Inf). Just remember, to be rigorous, that you need to use the notation of open set "( )" and closed set "[ ]" to be correct. Infinity is always used with the open set symbol as it can't be contained.

And yea... this stuff is probably never going to be useful to you. The sort of thinking MAY be useful in some areas but it's rare.
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      09-10-2013, 02:59 PM   #9
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Quote:
Originally Posted by scorcherjf View Post
You would simply state that the function is continuous over the ranges [-5,-3) and (-3,2]. More generally, the function is continuous everywhere except for x=-3 as you stated, which can formally be written as continuous over the ranges (-Inf,-3) and (-3,+Inf). Just remember, to be rigorous, that you need to use the notation of open set "( )" and closed set "[ ]" to be correct. Infinity is always used with the open set symbol as it can't be contained.

And yea... this stuff is probably never going to be useful to you. The sort of thinking MAY be useful in some areas but it's rare.
ah yes, i forgot the difference between "(" and "["
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      09-10-2013, 03:11 PM   #10
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This is probably the easiest part of Calc 1 too, lol. Wait until integrals and derivatives....
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      09-10-2013, 03:31 PM   #11
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Quote:
Originally Posted by Fifty3bags View Post
After a year of working as an engineer I can also confirm that this will not be needed. With that being said, I forgot everything from Calc I. Sorry
+1. Four years after graduation and not a single limit!
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      09-10-2013, 03:35 PM   #12
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Quote:
Originally Posted by F1Venom
This is probably the easiest part of Calc 1 too, lol. Wait until integrals and derivatives....
Integrals and derivatives were the best part of calculus. This stuff is the worst part. My favorite was probably double and triple integrals, but that's not calc I
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      09-10-2013, 03:37 PM   #13
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Quote:
Originally Posted by Fifty3bags View Post
Integrals and derivatives were the best part of calculus. This stuff is the worst part. My favorite was probably double and triple integrals, but that's not calc I
Discrete Math is my fav.
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      09-10-2013, 03:38 PM   #14
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Quote:
Originally Posted by Whostheboss
Quote:
Originally Posted by Fifty3bags View Post
Integrals and derivatives were the best part of calculus. This stuff is the worst part. My favorite was probably double and triple integrals, but that's not calc I
Discrete Math is my fav.
Worst class ever: Calc II. Fuck that Taylor Series bullshit
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      09-10-2013, 04:31 PM   #15
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Applied math theory...worst math class ever.
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      09-10-2013, 06:08 PM   #16
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anybody remember diff anal? pretty painful stuff.
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      09-10-2013, 06:38 PM   #17
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I can confirm as we'll this shit will never be used as an analyst at a Fortune 100 company. Fucking waste of time....I took calc 3...bullshit unless you're going to be a math teacher or some shit.
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      09-11-2013, 07:21 AM   #18
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I can confirm as we'll this shit will never be used as an analyst at a Fortune 100 company. Fucking waste of time....I took calc 3...bullshit unless you're going to be a math teacher or some shit.
Or engineer. Had to take all the math classes a math major would minus the little programming courses they have to take. Debated getting a math minor, but figured it'd be useless as an engineer.
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      09-11-2013, 08:38 AM   #19
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After 10 years at a major financial institution, I can confirm that this will never be used in your real life.
+1
same here
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      09-11-2013, 09:22 AM   #20
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Or engineer. Had to take all the math classes a math major would minus the little programming courses they have to take. Debated getting a math minor, but figured it'd be useless as an engineer.
I am a fucking engineer and can't remember how to solve that shit
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      09-11-2013, 10:35 AM   #21
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I am a fucking engineer and can't remember how to solve that shit
Engineer reporting in. I took up to Calc 4 in college and I can tell you unless you become a Calc professor, no need to remember any of it.

OP, wish I could help but that part of my brain is in retirement.
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      09-11-2013, 10:50 AM   #22
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Quote:
Originally Posted by F1Venom View Post
This is probably the easiest part of Calc 1 too, lol. Wait until integrals and derivatives....
It's mind blowing. I think I like Calculus II the best (I took up to Calculus III). Those 30-45 minutes to determine if it's converging or diverging problem days....

I do not miss one moment of it.

Welcome to hell OP... welcome to hell.
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