Need help with Calculus problem

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mobobuff

mobobuff

Lifer
Apr 5, 2004
11,099
1
81
This IS homework. It's not my homework, it's my girlfriend's homework. She's in AP Calc and I'm a tree stump when it comes to math outside of geometry. She's been stuck on this problem for a few days and feels really stupid because it should be easy, she's usually really good with this stuff. I told her there's a lot of advanced math people here, so against her will I MS-Painted the problem.

She's attempting to find the slope of a curve, here's all the information I could gather including what she has down already and what she's stuck at.

The problem

Don't ask me why she hasn't asked the teacher for help. But if any of you could help that would be greatly appreciated. :)
 
jman19

jman19

Lifer
Nov 3, 2000
11,225
664
126
Originally posted by: mobobuff
This IS homework. It's not my homework, it's my girlfriend's homework. She's in AP Calc and I'm a tree stump when it comes to math outside of geometry. She's been stuck on this problem for a few days and feels really stupid because it should be easy, she's usually really good with this stuff. I told her there's a lot of advanced math people here, so against her will I MS-Painted the problem.

She's attempting to find the slope of a curve, here's all the information I could gather including what she has down already and what she's stuck at.

The problem

Don't ask me why she hasn't asked the teacher for help. But if any of you could help that would be greatly appreciated. :)
Click to expand...

Get rid of h from the denominator (so that you don't divide by 0) and see what you get as h->0.
 
mobobuff

mobobuff

Lifer
Apr 5, 2004
11,099
1
81
Originally posted by: jman19
Originally posted by: mobobuff
This IS homework. It's not my homework, it's my girlfriend's homework. She's in AP Calc and I'm a tree stump when it comes to math outside of geometry. She's been stuck on this problem for a few days and feels really stupid because it should be easy, she's usually really good with this stuff. I told her there's a lot of advanced math people here, so against her will I MS-Painted the problem.

She's attempting to find the slope of a curve, here's all the information I could gather including what she has down already and what she's stuck at.

The problem

Don't ask me why she hasn't asked the teacher for help. But if any of you could help that would be greatly appreciated. :)
Click to expand...

Get rid of h from the denominator (so that you don't divide by 0) and see what you get as h->0.
Click to expand...

Thanks, she wrote that out on her paper to ponder it. Still stuck though.

Anyone else got any ideas?
 
nycxandy

nycxandy

Diamond Member
Apr 11, 2001
3,731
0
76
When h approaches 0, the top and bottom both approach 0. Thus it's 0/0. Use L'Hopital's Rule to solve it. Have fun!
 
D

Dowfen

Senior member
Jul 16, 2002
284
0
0
Originally posted by: nycxandy
When h approaches 0, the top and bottom both approach 0. Thus it's 0/0. Use L'Hopital's Rule to solve it. Have fun!
Click to expand...

My guess is that she hasn't even gotten to derivatives, which basically means no L'hopital's rule...
 
C

Chronoshock

Diamond Member
Jul 6, 2004
4,860
1
81
Originally posted by: nycxandy
When h approaches 0, the top and bottom both approach 0. Thus it's 0/0. Use L'Hopital's Rule to solve it. Have fun!
Click to expand...

Not quite, for this assignment you'll want to cross multiply by x-1 and x+h-1 to get rid of the denominators on top. After that you can factor and solve for the specific case (sub 2 in for x)

So this is what you do:
(1/(x-1+h)-1/(x-1))/h
= (x-1 - (x - 1 + h))/(h*(x-1)(x-1+h))
= -h/(h*(x-1)(x-1+h))
= -1/((x-1)(x-1+h))
= -1/(x-1)^2 as h -> 0
which is the correct answer if you simply took the derivative
plug in 2 for x and you get -1/1^2 = -1
 
nycxandy

nycxandy

Diamond Member
Apr 11, 2001
3,731
0
76
Originally posted by: Chronoshock
Originally posted by: nycxandy
When h approaches 0, the top and bottom both approach 0. Thus it's 0/0. Use L'Hopital's Rule to solve it. Have fun!
Click to expand...

Not quite, for this assignment you'll want to cross multiply by x-1 and x+h-1 to get rid of the denominators on top. After that you can factor and solve for the specific case (sub 2 in for x)
Click to expand...

Sounds good.
 
R

rgwalt

Diamond Member
Apr 22, 2000
7,393
0
0
OK, I'm going to do my best to type this out...

(1/(2+h-1) - 1/(2-1))/h =

(1/(h+1) - 1/1)/h =

Multiply 1/1 by (h+1)/(h+1)

(1/(h+1) - (h+1)/(h+1))/h =

Combine the numerator terms

((1-(h+1))/(h+1))/h =

Simplifying

(-h/(h+1))/h =

Simplifying further

-1/(h+1)

Subbing h=0

-1/(0+1) = -1/1 = -1

This is the correct answer if you take the derivative of y with respect to x and evaluate it at x = 2.

R
 
P

PoPPeR

Diamond Member
Oct 9, 2002
6,993
0
0
Calculus actually wasn't too hard for me. If I had a solid algebra foundation it would've been a breeze. Ugh... dividing by square roots and crap... the horror
 
C

Chronoshock

Diamond Member
Jul 6, 2004
4,860
1
81
Originally posted by: rgwalt
OK, I'm going to do my best to type this out...

(1/(2+h-1) - 1/(2-1))/h =

(1/(h+1) - 1/1)/h =

Multiply 1/1 by (h+1)/(h+1)

(1/(h+1) - (h+1)/(h+1))/h =

Combine the numerator terms

((1-(h+1))/(h+1))/h =

Simplifying

(-h/(h+1))/h =

Simplifying further

-1/(h+1)

Subbing h=0

-1/(0+1) = -1/1 = -1

This is the correct answer if you take the derivative of y with respect to x and evaluate it at x = 2.

R
Click to expand...


Yup, got the same answer
 
TuxDave

TuxDave

Lifer
Oct 8, 2002
10,571
3
71
Dude... this doesn't use any calculus.

The numerator is 1/[(2+h)-1]-1/(2-1) = 1/(1+h)-1 = 1/(1+h)-(1+h)/(1+h) = -h/(1+h)
The denominator = h

The fraction becomes - 1/(1+h) ---> -1

QED!

Edit GOD DAMMIT!!! I'm slow....
 
E

Ender

Golden Member
Jul 24, 2001
1,694
0
0
Lol my AP class did that a week ago. It was easy stuff compared to what we're doing now.
 
silverpig

silverpig

Lifer
Jul 29, 2001
27,703
12
81
Originally posted by: Mo0o
So you're not allowed to use derivatives?
Click to expand...

Have you never seen the definition of the derivative? This IS the derivative, worked out formally. All those derivative rules you learned come from this. This is like... the essence of calculus right here.
 
E

Ender

Golden Member
Jul 24, 2001
1,694
0
0
Originally posted by: Mo0o
So you're not allowed to use derivatives?
Click to expand...

In my AP class, our teacher didn't let use the differential formulae (the shortcuts, essentially) until we mastered derivative #1 by definiton (the above equation). Otherwise this would obviously be much easier.
 
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