GRE 0568 #4)

Forum for the GRE subject test in mathematics.
Philochorus
Posts: 2
Joined: Fri Jul 31, 2009 10:29 am

GRE 0568 #4)

Postby Philochorus » Fri Jul 31, 2009 10:34 am

How do i solve this equation without graphing on a computer or calculator:

(e^x)+x-2=0

?

This equation appears on GRE 0568, #4)

Thanks.

User avatar
lime
Posts: 129
Joined: Tue Dec 04, 2007 2:11 am

Re: GRE 0568 #4)

Postby lime » Fri Jul 31, 2009 11:36 am

Consider continuous function

f(x) = exp(x) + x - 2.

Its derivative is always positive. Hence, the function is monotonous, increasing and, as result, might have only one root. Secondly,

f(0) = -1 < 0;
f(1) = e - 1 > 0.

Hence, its only root is inside interval [0, 1].




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