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Dido525 Group TitleBest ResponseYou've already chosen the best response.1
the following function is differentiable for all values of x.
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.1
dw:1350070251929:dw
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.1
I figured out a= 1 but I can't figure out what b is equal to.
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.1
Oops. I figured out b = 1.
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.1
I can`t solve for a.
 2 years ago

myininaya Group TitleBest 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.
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Because one this it must need to be is continuous
 2 years ago

Dido525 Group TitleBest 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.
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.1
Should I derive both functions and solve for a?
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.1
But that just means it's continuous. Not differentiable.
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Right that is one condition we must need though
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
We need it to run smoothly when they meet (no sharp corners)... hmm... thinking....
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.1
So I go: dw:1350070954216:dw
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.1
right? O_o .
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.1
No. Thats not right.
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.1
Never mind.
 2 years ago

myininaya Group TitleBest 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
 2 years ago

Dido525 Group TitleBest 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.
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
\[(\arctan(ax+1))'_{x=0}=(\frac{\pi}{4} e^{\sin(x)})'_{x=0}\]
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.1
I tried that.
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Find derivative of both sides Set x=0 And solve you are done
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.1
Let me try again. Maybe I made a mistake.
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.1
The derivative of arctan(ax+1) dw:1350071299130:dw right?
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Is that an a on top ?
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.1
It shoud say 1/(1+(ax+1)^2)
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
no it should say a on top
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
that is your issue
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
(ax+1)'=a
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.1
haha... Chain rule.... oops.
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
\[(\arctan(u(x))'=\frac{u'(x)}{{1+(u(x))^2}}\]
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.1
so it would be \[\frac{ a }{ 1+(ax+1)^2 }\]
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Yep and the other side you have?
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.1
dw:1350071580411:dw
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.1
I really appreciate the help by the way. Thanks a lot.
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
I think you got it from here :) Great job.
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.1
I got a = pi/2
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.1
@myininaya .
 2 years ago

Dido525 Group TitleBest ResponseYou've already chosen the best response.1
Thanks for making this so easy to understand! :) .
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
That is what I got :)
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Gj again.
 2 years ago
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