My Math Forum Stuck at solving equation

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 September 20th, 2018, 11:32 AM #1 Newbie   Joined: Sep 2018 From: Sweden Posts: 6 Thanks: 0 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.
 September 20th, 2018, 11:44 AM #2 Senior Member   Joined: Sep 2016 From: USA Posts: 562 Thanks: 325 Math Focus: Dynamical systems, analytic function theory, numerics Just apply Newton's method. This gives a solution $x = .7921...$. Since the expression is monotone increasing, this must be a unique solution.
 September 20th, 2018, 11:50 AM #3 Newbie   Joined: Sep 2018 From: Sweden Posts: 6 Thanks: 0 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.
 September 20th, 2018, 11:53 AM #4 Newbie   Joined: Sep 2018 From: Sweden Posts: 6 Thanks: 0 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.
 September 20th, 2018, 02:14 PM #5 Global Moderator   Joined: May 2007 Posts: 6,685 Thanks: 661 The equation has no analytic solution, only numerical.
 September 20th, 2018, 02:37 PM #6 Newbie   Joined: Sep 2018 From: Sweden Posts: 6 Thanks: 0 Ok, but how to I proceed to solve it numerical?
September 20th, 2018, 02:37 PM   #7
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 Originally Posted by Trigger12 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?

September 20th, 2018, 02:38 PM   #8
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 Originally Posted by JeffM1 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.

September 20th, 2018, 02:46 PM   #9
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 Originally Posted by Trigger12 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.

September 20th, 2018, 02:55 PM   #10
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 Originally Posted by JeffM1 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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