Let and be defined on

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let

f(x)=\ln x

and

g(x)=kx-1

be defined on

[1,e]

, where

k

is a real parameter. For which of the following ranges of

k

is it guaranteed that

f(x)=g(x)

has at least one solution in

(1,e)

? (a)

k>1

(b)

\dfrac{2}{e}<k<1

(c)

0<k<\dfrac{2}{e}

(d)

k<0