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Loser66
 one year ago
How many solutions are there on \(sec (x) = e^{x^2}\)
Please, help
Loser66
 one year ago
How many solutions are there on \(sec (x) = e^{x^2}\) Please, help

This Question is Closed

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1Another confusing; \(x^2+4x15=0\) have 2 solutions, but if we apply Decartes rule, we have only 1 real solution. What is wrong? dw:1438396954345:dw

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1Thanks for replying. There are some problems: 1) I open your link and see nothing 2) my link shows it has only 1 solution. https://www.desmos.com/calculator/bnyfuxsluv 3) I would like to know how to solve it by hand.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1Oh, I see your mistake, it is \(sec (x) = e^{x^\color{red}{2}}\), while you put \(e^{x/2}\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3dw:1438397782196:dw

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1@ganeshie8 I got it :)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3for the first problem, you may try showing that \(\sec(x)\ge 1\) and \(e^{x^2}\le 1\) and use first derivative to show that \(e^{x^2}\) is decreasing on either side of its "only" maximum value

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1@ganeshie8 I don't get it. Why we have to do that?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Both are well known graphs, use that knowledge to your advantage in ur proof. The reasoning goes like this : I know that \(e^{x^2}\) is a bell shaped graph which stays above x axis and below y=1. I also know that \(\sec x\ge 1\). So I want use these two facts in my proof (ofcourse you need to prove these facts in ur proof too)

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1I understood @ganeshie8 Thank you so much.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3np, small correction : for the first problem, you may try showing that \(\color{red}{}\sec(x)\color{red}{}\ge 1\) and \(e^{x^2}\le 1\) and use first derivative to show that \(e^{x^2}\) is \(\color{red}{\text{strictly}}\) decreasing on either side of its "only" maximum value
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