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Dido525
 2 years ago
Find a and b such that
Dido525
 2 years ago
Find a and b such that

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

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

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

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

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

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1Yep . I set the both as lim x> 0 and I got that b = 1. I can't solve for a however.

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

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

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

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

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

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1Ok...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

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.1Yep. I knew that. But unless I know what a is equal to I can't solve for the derivative at x=0.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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