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Question: For the smallest positive root of transcendental equation \(x - e^{- x} = 0\), interval is...

For the smallest positive root of transcendental equation x−e−x=0x - e^{- x} = 0, interval is

A

(0, 1)

B

(–1, 0)

C

(1, 2)

D

(2, 3)

Answer

(0, 1)

Explanation

Solution

Let f(x)=x−e−x=0⇒xex−1=0f(x) = x - e^{- x} = 0 \Rightarrow xe^{x} - 1 = 0 but f(0)=−ivef(0) = - ive and

f(1)=+ivef(1) = + ive. Therefore root lie in (0,1).