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# Can Anyone solve this Calculus Problem!?!?! (1 Viewer)

#### Jin E

##### Second Unit
I admit, my calculus is a bit fuzzy after not having it in over 8 years. But, since my girlfriend is taking a Calculus class I've found that I know a lot more about math and calculus then I thought I did. So far I've been able to answer every question she's had, cept for this one. When all else fails, turn to the Home Theater Forum collective for help.... so here goes.

The problem ask for the values of a and b so that:

Limit [(ax-b)^(1/2) - 3] / x = 2
(x->0)

#### AviTevet

##### Stunt Coordinator
she's promised me conjugal relations.
I'll only post the answer if I can get in on this.
Man I am rusty at algebra!
Here's the deal. Since you have only one equation but two unknowns, there are infinitely many sets of (a, b) pairs that satisfy the conditions set forth in the problem. Which raises the obvious question "if there are infinitely many, why can't I find any of them?" Well, you just have to pick one of them (blindly) by assigning "b" a convenient value and hoping "a" will be easy to find once b is known. YOu can choose any value for b, like 34.7, pi, or 0.004, but personally I chose -9 .
And don't forget L'Hopital's rule:
For f(x) and y(x) where f(0)=0 and y(0)=0,
lim f(x)/y(x) ==
(x->0)
lim f'(x)/y'(x)
(x->0)

#### PhilipG

Senior HTF Member
Looks like we have a notation difference between US & UK. So I'm assuming you're taking the differential of the term in square brackets and x is greater than 0? Multiply both sides by x. Integrate the rhs. Square both sides. Reorder. I get
x^4 + 6x^2 -ax + ( 9 + b ) = 0
So there's Avi's b=-9

#### Jonathan Smith

##### Stunt Coordinator
Avi's method should get you a correct answer. I'm pretty sure it is the only one, not one of an infinite set like he suggests.
I get a=12 and b=-9
If anyone can post different values that work, I would be surprised

#### Jeff Kleist

Senior HTF Member
Sorry, Calculus is HARD!
(see Jack Briggs' science post)

#### Jed M

Senior HTF Member
Now I remember why I majored in Political Science.

#### Chuck C

Senior HTF Member
I also get a=12 and b= -9
The work: (assume lim = lim as x approaches 0)
using l'hospital's rule :
lim ½a(ax-b)^(-½) = 2
lim a(ax-b)^(-½) = 4
a(-b)^(-½) = 4
a/(-b^½) = 4
12/3 = 4
yay!
now have some fun with your amiga

#### Mike St.Louis

##### Supporting Actor
I got a = 12 and b = -9

----

(((ax - b)^1/2) - 3)/x = 2
(ax - b)^1/2 - 3 = 2x
(ax - b)^1/2 = 2x + 3
(ax - b) = (2x + 3)^2
(ax - b) = 4x^2 + 12x + 9

lim x -> 0
b = -9

Substituting b = -9 and resolving:

ax + 9 = 4x^2 + 12x + 9
ax = 4x^2 + 12x
a = 4x + 12

lim x ->0
a = 12

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