Stuck at solving equation

Sep 2018
6
0
Sweden
Hi.

I can't find an answer to the equation \(\displaystyle e^x+x-3=0\). I'm not sure how to solve it.
 
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SDK

Sep 2016
797
541
USA
Just apply Newton's method. This gives a solution $x = .7921...$. Since the expression is monotone increasing, this must be a unique solution.
 
Sep 2018
6
0
Sweden
I have already done that in the second question where they tell you to use Newton´s method. But the first question is: Show that we can find the value of a, solving the equation e^x+x-3=0.
 
Sep 2018
6
0
Sweden
The task is:
The tangent to the curve \(\displaystyle y=e^{2-x} \) in \(\displaystyle x=2 \) cuts the curve \(\displaystyle y=e^x \) in a point where x=a.
 
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mathman

Forum Staff
May 2007
6,932
774
The equation has no analytic solution, only numerical.
 
Sep 2018
6
0
Sweden
Ok, but how to I proceed to solve it numerical?
 
May 2016
1,310
551
USA
I have already done that in the second question where they tell you to use Newton´s method. But the first question is: Show that we can find the value of a, solving the equation e^x+x-3=0.
Have you thought about applying the mean value theorem to the function

$f(x) = e^x + x - 3.$

Is f(x) continuous?

What is the sign of f(0)?

What is the sign of f(1)?

What does all that imply about the existence of a such that f(a) = 0?
 
Sep 2018
6
0
Sweden
Have you thought about applying the mean value theorem to the function

$f(x) = e^x + x - 3.$

Is f(x) continuous?

What is the sign of f(0)?

What is the sign of f(1)?

What does all that imply about the existence of a such that f(a) = 0?
Ahh! I didn't think about solving it that way.
 
May 2016
1,310
551
USA
Ahh! I didn't think about solving it that way.
Without understanding the exact language of the problem, I cannot be sure my suggestion is even partially relevant. And my Swedish is non-existent so you are on your own in terms of judging how helpful the suggestion is.
 
Sep 2018
6
0
Sweden
Without understanding the exact language of the problem, I cannot be sure my suggestion is even partially relevant. And my Swedish is non-existent so you are on your own in terms of judging how helpful the suggestion is.
In the second question, I used Newton's method to find an approximate value of a, and got 0,792059, that is correct. My problem is that they want us to find the same value, but by solving the equation given over in the first question.
 
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