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Need help with Calculus problem

mobobuff

mobobuff

Lifer
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. 🙂
 
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.
 
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?
 
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!
 
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...
 
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
 
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.
 
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
 
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
 
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
 
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....
 
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.
 
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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