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September 20th, 2018, 11:32 AM   #1
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Stuck at solving equation

Hi.

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

Last edited by skipjack; September 20th, 2018 at 06:55 PM.
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September 20th, 2018, 11:44 AM   #2
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Just apply Newton's method. This gives a solution $x = .7921...$. Since the expression is monotone increasing, this must be a unique solution.
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September 20th, 2018, 11:50 AM   #3
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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.
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September 20th, 2018, 11:53 AM   #4
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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.

Last edited by skipjack; September 20th, 2018 at 06:57 PM.
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September 20th, 2018, 02:14 PM   #5
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The equation has no analytic solution, only numerical.
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September 20th, 2018, 02:37 PM   #6
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Ok, but how to I proceed to solve it numerical?
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September 20th, 2018, 02:37 PM   #7
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Quote:
Originally Posted by Trigger12 View Post
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?
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September 20th, 2018, 02:38 PM   #8
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Quote:
Originally Posted by JeffM1 View Post
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.
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September 20th, 2018, 02:46 PM   #9
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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.
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September 20th, 2018, 02:55 PM   #10
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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.

Last edited by skipjack; September 20th, 2018 at 07:11 PM.
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