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Dido525Best ResponseYou've already chosen the best response.1
the following function is differentiable for all values of x.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
I figured out a= 1 but I can't figure out what b is equal to.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Oops. I figured out b = 1.
 one year ago

myininayaBest ResponseYou've already chosen the best response.1
Yep. Now that is right so far. You just set the limx>0 for both of them and solve for a b. Good job.
 one year ago

myininayaBest ResponseYou've already chosen the best response.1
Because one this it must need to be is continuous
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Yep . I set the both as lim x> 0 and I got that b = 1. I can't solve for a however.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Should I derive both functions and solve for a?
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
But that just means it's continuous. Not differentiable.
 one year ago

myininayaBest ResponseYou've already chosen the best response.1
Right that is one condition we must need though
 one year ago

myininayaBest ResponseYou've already chosen the best response.1
We need it to run smoothly when they meet (no sharp corners)... hmm... thinking....
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
So I go: dw:1350070954216:dw
 one year ago

myininayaBest ResponseYou've already chosen the best response.1
Ok...how about this : What do you think of both parts of the function having the same exact slope at x=0 This will give us that smooth transition at x=0 that i'm talking about
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Yep. I knew that. But unless I know what a is equal to I can't solve for the derivative at x=0.
 one year ago

myininayaBest ResponseYou've already chosen the best response.1
\[(\arctan(ax+1))'_{x=0}=(\frac{\pi}{4} e^{\sin(x)})'_{x=0}\]
 one year ago

myininayaBest ResponseYou've already chosen the best response.1
Find derivative of both sides Set x=0 And solve you are done
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Let me try again. Maybe I made a mistake.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
The derivative of arctan(ax+1) dw:1350071299130:dw right?
 one year ago

myininayaBest ResponseYou've already chosen the best response.1
Is that an a on top ?
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
It shoud say 1/(1+(ax+1)^2)
 one year ago

myininayaBest ResponseYou've already chosen the best response.1
no it should say a on top
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
haha... Chain rule.... oops.
 one year ago

myininayaBest ResponseYou've already chosen the best response.1
\[(\arctan(u(x))'=\frac{u'(x)}{{1+(u(x))^2}}\]
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
so it would be \[\frac{ a }{ 1+(ax+1)^2 }\]
 one year ago

myininayaBest ResponseYou've already chosen the best response.1
Yep and the other side you have?
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
I really appreciate the help by the way. Thanks a lot.
 one year ago

myininayaBest ResponseYou've already chosen the best response.1
I think you got it from here :) Great job.
 one year ago

Dido525Best ResponseYou've already chosen the best response.1
Thanks for making this so easy to understand! :) .
 one year ago

myininayaBest ResponseYou've already chosen the best response.1
That is what I got :)
 one year ago
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