Question

If f(x) = ln(x^2 + 1) , find the number a (exact) such that f(3)−f(1)/(3−1) = ln a

Answer 1

Step 1:

Find the value of f (3) :

f ( x ) = ln ( x² + 1 )

         = ln ( 3² + 1 )

         = ln 10

         = 2.3026

Find the value of f (1) :

f ( 1 ) = ln ( x² + 1 )

         = ln ( 1² + 1 )

         = ln 2

         = 0.69315

Step 2:

Find the value of a :

Substitute 2.3026 for f ( 3 ) and 0.69315 for f ( 1 ).

Solution:

The value of a is 2.24.