For 1 y l n ( y ) l n ( x ) y x 1 x f ( t ) l n ( t ) , 0 , 0 y f ( t ) l n ( t ) 1 x 1 c 0 1 y 1 y 1 y l n ( y ) l n ( x ) y x 1 x 0 , then 1 x D 1 c 0 1 y 1 y S o 1 y l n ( y ) l n ( x ) y x 1 x Need Help x For f ( t ) l n ( t ) , this i s 0 0 Because 0 , then 1 x D 1 c 0 1 y 1 y S o 1 y l n ( y ) l n ( x ) y x 1 x Need Help x , y , 0 B y the Mean Value Theorem, , 0 , 0 y for x For f ( t ) l n ( t ) , this i s 0 0 Because 0 , then 1 x D 1 c 0 1 y 1 y S o 1 y l n ( y ) l n ( x ) y x 1 x Need Help 0 , use the Mean Value Theorem t o show that 1 y l n ( y ) l n ( x ) y x 1 x Let f ( t ) l n ( t ) o n x , y , 0 B y the Mean Value Theorem, , 0 , 0 y for x For f ( t ) l n ( t ) , this i s 0 0 Because 0 , then 1 x D 1 c 0 1 y 1 y S o 1 y l n ( y ) l n ( x ) y x 1 x Need Help

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Question: For 1 y l n ( y ) - l n ( x ) y - x 1 x f ( t ) = l

For

\frac{1}{y} \frac{l n (y) - l n (x)}{y - x}\frac{1}{x}f(t)=ln(t)\frac{?, 0 - ?, 0}{y -}=f(t)=ln(t)\frac{1}{x}\frac{1}{c}0\frac{1}{y}\frac{1}{y}\frac{1}{y}\frac{l n (y) - l n (x)}{y - x}\frac{1}{x}0,

then

\frac{1}{x} D \frac{1}{c} ? 0 \frac{1}{y} \frac{1}{y} . S o \frac{1}{y} \frac{l n (y) - l n (x)}{y - x}\frac{1}{x}.

Need Help?

x .

For

f (t) = l n (t),

this

i s ? 0 - ? 0

Because

0,

then

\frac{1}{x} D \frac{1}{c} ? 0 \frac{1}{y} \frac{1}{y} . S o \frac{1}{y} \frac{l n (y) - l n (x)}{y - x}\frac{1}{x}.

Need Help?

[x, y], 0 .

B y

the Mean Value Theorem,

\frac{?, 0 - ?, 0}{y -} =

for

x .

For

f (t) = l n (t),

this

i s ? 0 - ? 0

Because

0,

then

\frac{1}{x} D \frac{1}{c} ? 0 \frac{1}{y} \frac{1}{y} . S o \frac{1}{y} \frac{l n (y) - l n (x)}{y - x}\frac{1}{x}.

Need Help?

0,

use the Mean Value Theorem

t o

show that

\frac{1}{y} \frac{l n (y) - l n (x)}{y - x}\frac{1}{x}

Let

f (t) = l n (t) o n [x, y], 0 .

B y

the Mean Value Theorem,

\frac{?, 0 - ?, 0}{y -} =

for

x .

For

f (t) = l n (t),

this

i s ? 0 - ? 0

Because

0,

then

\frac{1}{x} D \frac{1}{c} ? 0 \frac{1}{y} \frac{1}{y} . S o \frac{1}{y} \frac{l n (y) - l n (x)}{y - x}\frac{1}{x}.

Need Help?

For 1 y < l n ( y ) - l n ( x ) y - x < 1 x f ( t

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